Please imagine the following scenario: you go to a store, buy a DVD and in that DVD you find a note, that a Director's Cut of the movie, you have just bought, is being planned. That is just what happened in the USA to the buyers of the first Zodiac-DVD. Disappointment and anger may be understandable and, of course, you inevitably wonder, if you should spend any more money on that movie, again.
The answer, however, is almost taken away from you. Everybody, who attaches importance to bonus features, will have to consider the Director's Cut, since it has way more bonus features on the second disc and an audio-commentary on the first one.
All, that is left, is the question, if a Director's Cut to Fincher's newest creation makes sense, after all. This serial-killer-thriller is rather a perfect refurbishment and a minutious narration of what happened in the 60ies and 70ies, and the analysis of the characters of those, who were fascinated by the killer, is way more at center than the killer himself, and with almost 2.5 hours, it is not exactly short, in the Theatrical Version already.
Now we find approximately five more minutes of new footage in the Director's Cut, which is mostly kind of insignificant, meaning dialogue-extensions, and so not really capable of adding any new details to the story.
Only the three longer changes are of interest. There is a new scene between Graysmith and Avery, that makes Avery's slow degeneration clear, while , a little later, we get closer insight of Toschi's and Armstrong's police-work, how they get the search warrant for Allen's apartment, which is hardly dealt with in the Theatrical Version.
Also the montage over the black frame is something, that I in particular would not want to miss, since it clarifies to the audience the ingenious dealing with and showing time in this movie.
Those, who did not care much about the movie in the Theatrical Version, will not be made into fans by the DC - even though I would still recommend a second viewing of this movie.
For everybody else, the DC and especially the DVD is a real alternative.

About the report itself, should be said , that it is a comparison between the German "FSK-16" DVD DVD which includes the theatrical version and the American 2-Disc Director's Cut, which causes the usual PAL Speed-up problem, when dealing with corresponding shots in the two versions. This is why I prefer telling you, that the versions are different in ten scenes. The information about the running time before the cuts refer to the German DVD and are only information, where something new is happening in the DC. Scenes in red show, that something is missing in the DC.

Note from the translator:
Abbreviations, being used:
DC: Director's Cut
TV: Theatrical version

43:20

The first change can be found during the live-broadcast of the TV-Show, when the Zodiac-killer calls. A little piece of dialogue between Melvin Belli and the Zodiac was reinserted:

Melvin, has just asked him, if he has a less ominous name. The camera shows inspector Toschi in the observation room: "Is there somewhere we can meet, Sam, and talk about this?"- In the TV there is this scene, too, but another off-text was put over it, namely Belli's question, if Sam/Zodiac needs medical help.
POV of Toschi, looking at Armstrong, who is looking back at him. New footage from here on. During that, we still hear the Zodiac from the off: "Meet me on top of the Fairmont Hotel."
Then Toschi grabs the receiver and informs the units, while the Zodiac continues with: "Without anyone else or I'll jump...".
Now Toschi: "Have a unit go to the Fairmont Hotel."
Until the moment, when the images in both versions start being parallel again, the DC contains different shots during Belli's question about his state of health. All in all, the scene enlargement contains:
14 sec.

44:29

Again, the Zodiac speaks longer in the DC. After the question, how long he has been having the headaches and his answer: "Since I killed a kid.", the following happens in the TV:
A short cutaway to Belli and his co-commentator, then cut to Graysmith. In the DC, however, the following happens: Avery can be seen longer, while Belli is asking from the off: "Do you have blackouts?"
Zodiac: "Yes."
Cutaway to the studio. Belli: "Do you have fits?"
Zodiac: "No, I just have headaches."
Then the co-commentator: "Did you attempt to call one other time when F. Lee Bailey was with us two or three weeks ago?"
Zodiac: "Yes."
Co-commentator: "And why did you want to talk to Mr. Bailey?"
Belli: "Why do you wanna talk to me, Sam?"
Then the cutaway to Graysmith.
17 sec.

52:16

In the DC, there is a little more dialogue and information in the scene of Toschi and Armstrong visiting Belli at home, because he received a letter from the Zodiac. After he was asked, when exactly the letter arrived at his home, Belli goes a bit more into detail:
Belli: "I was away on safari. What did you gentlemen do for Christmas?"
Toschi: "You're looking at it."
Belli: "You must see Africa. Cradle of civilization. Fascination people. Beautiful. Savage."
Armstrong: "Back to the killer who wrote to you."
Belli: "Yes. Of course."
15 sec.

69:18

After Avery has dug up further information, he, Toschi and some other policemen, who are involved in the case, fly to Riverside, to look at the files there. How Toschi meets the chief of police and the resulting short dialogue are missing in the TV.
Toschi, entering the station: "Cross? Hi."
Captain Cross: "Yeah."
Toschi: "Detective David Toschi, SFPD."
Cross: "How are you doing?"
Toschi: "Great. Thanks for having us down today."
Cross: "Not at all. I hear you have some files for us."
Toschi: "I'll show you mine. You show me yours."
Cross: "Frisco, right?"
Toschi: "That's right. San Francisco."
They start moving
Toschi: "Ken Narlow from Napa."
Cross, says hello: "Ken."
Toschi: "Mel Nicolai, Justice."
Cross, says hello: "Mel."
17 sec.

69:33

Captain Cross tells some more details about the first Zodiac-murder:

Cross: "Her car is disabled. Someone cut the coil in the distributor, the battery died. Then someone comes back, offers help."
Toschi: "Like Kathleen Johns."
Cross: "Who?"
Narlow: "A woman outside of Modesto, might be a Zodiac victim."
Toschi, takes the file: "Might. Might be. I have her comp right here in this file." He moves the file to Cross.
Cross: "Okay."
At the transition to parallelism, Cross is being seen earlier, telling about the confession, in the DC. In the TV, however, a short reverse shot of the group has been taken out.
15 sec.

84:03

After Toschi and Armstrong have interrogated Leigh and have been told, that they have to find more evidence, a whole scene between Graysmith and Avery is missing in the TV, afterwards.

Graysmith sees Avery's car standing in front of his local, he walks over to it and knocks on the pane. Avery, visibly hung over, scares up and opens the window a little bit.
Avery: "Christ, kid. Yeah."
Graysmith: "Paul, I've been thinking..."
Avery: "Oh, God save us all."
Graysmith: "The letter to Melvin Belli was sent exactly one year after the Lake Herman Road murder. And the one to Cheri Jo Bates' father was sent exactly six months after her death. She was killed a day before Halloween."
Avery: "Yeah."
Graysmith: "Any you received a Halloween card..."
Avery: "You know, these are all fascinating pieces of news, Robert, it's a bit early in the day."
Graysmith: "Paul, it's 11:00 and we missed Editorial."
After that, Avery gets out of the car quickly and the two leave the scenery.
Graysmith: "I'm sorry. I didn't mean to wake you up."
Paul: "No, no, no."
Graysmith: "I just thought that..."
Paul: "No, no, no."
43 sec.

89:01

A longer interlocution with the district attorney is following, after Toschi and Armstrong have rechecked their suspicious facts against Leigh, after having persecuted other hints for a year. In the TV, we only see them, receiving the search warrant, that has already been signed:
Armstrong: "Suspect is Arthur Leigh Allen. Lives in Sunset Trailer Court in Santa Rosa, California. Physical description. Allen is similar in height, weight and build to a man seen at Lake Berryessa on the day of the stabbings."
DA, via speaker: "I understand he doesn't look much like the San Francisco composite."
Armstrong: "True, height and weight are sketchy, but lumbering Caucasian with a crew cut is right on."
Toschi: "We never had much confidence in the composite from the kids. The patrolman who saw Zodiac that night said he didn't look much like the sketch."
Armstrong: "Military boot prints. Allen was in the Navy. Wears a size 10-and-a-half. Same size as the prints in Berryessa."
DA: "What about the gun?"
Armstrong: "Cheney says Allen owns several firearms. We'll list them in the warrant."
DA: "And the ciphers?"
Armstrong: "Could be code training in the Navy and people have seen Allen with ciphers in the past."
DA: "Really? Who?"
Toschi: "That would be his sister-in-law and a man named Phil Tucker that he worked with at a public pool in Vallejo."
Armstrong: "And Phil Tucker told us about a conversation that he had with Allen about how to attach a flashlight to the barrel of a gun."
Captain: "That gives us two sources on the ciphers and two on the flashlight."
DA: "What about his threats on children?"
Captain: "Suspect worked for elementary schools and was fired for molestation in March, April '68. Could give him motive."
Armstrong: "At the very least, it's home turf. He'd have knowledge of bus routes, which the two major threats centered around."
DA: "What about the bomb?"
Armstrong: "Allen works as a chemist."
Captain: "Take him through the geography."
Armstrong: "Vallejo murders. Allen lives in Vallejo with his mother in her basement. Berryessa murder. On the day that the two kids were stabbed his neighbor saw bloody knives in his truck which he claimed were used to kill a chicken."
DA: "Does he have any alibis?"
Armstrong: "He claimed he did, but he's been unable to produce the names of the couple he supposedly met on the day of Berryessa."
Toschi: "The bottom line is that Allen can't alibi up on anything. Riverside, Vallejo, the lake or us. You want to tell me about the name?"
DA: "What name?"
Armstrong: "Zodiac. Allen wears a watch that bears both the word and crosshair symbol. And he mentioned Zodiac to Cheney a year and a half before it appeared in any letter."
Captain: "John..."
DA: "That's pretty good, guys."
Captain: "We think so, too."
DA: "Let's take it to a judge."
129 sec.

89:01

Because of the very detailed refurbishment of the investigation, the scene, showing the signed paper on the desk, is missing, in the DC.
Judge, from the off: "Well, it looks like you got your man." After that, the search follows in both versions.
4 sec.

94:34

Now the very ingenious montage over the black frame was shortened in the TV, while voice-overs clarify, that four more years have passed, in the DC. This was done by playing contemporary songs and adding a montage of different news anchors, reading recognizable news:
To America's "A Horse With No Name" we hear: "We today have concluded an agreement to end the war and bring peace with honor to Vietnam."
Followed by The Temptations with "Papa Was A Rollin' Stone" and the text: ...Charles Manson for the Tate-La Bianca mass murders..." Another voice: "Guilty in the Chowchilla kidnapping case." "In the murder trial of one..."
Another change to Roberta Flack's "Killing me Softly": "Chairman Mao died today..." "... an absolute pardon unto Richard Nixon..." "... -No I'm not a crook..." "...Generation of hostility..."
Yet another change: "... has now led to the death of 50.000 Americans and several hundred thousand Vietnamese."
Another montage and to Bachman-Turner Overdrive's "You Ain't Seen Nothing Yet": "Patricia Hearst is kidnapped by the Symbionese Liberation Army..." "All of us should stand up together and say, "No more."
And again: "Your Declaration of Independence spreads that..." "Americans admire the United Kingdom..." "Mr. Hoffa has disappeared."
And for the last time, the song changes: "If we despise our own government... "...that the police have captured a man whom they believe to be the "Son of Sam"..."
After that a flash of text: "four years later".
59 sec.

134:05
After Graysmith has visited Linda in prison and she destroys his evidence concerning Rick Marshalls, we see Graysmith, sitting there a few seconds longer, before he gets up, in the DC.
6 sec.