Time difference (Theatrical Cut): 12 cuts = 3 min. 17 sec.
Time difference (DVD Edition): 02 cuts = 0 min. 06 sec.

For the DVD release of the first "Star Wars" movie, some new scenes were added by George Lucas.

0:53:24
The champion jumps on his pod racer and the crowd cheers at him. He sends kisses to the audience.
( 6 Sec. )

0:53:29
Here is a difference between the Theatrical Cut and the DVD Edition:

DVD Edition: The announcer introduces more participators of the race.
( 35 Sec. )

Theatrical Cut: Shot of some cheering aliens.
Addition (Glogcke):
When you look very carefully at the crowd you can recognize the midget actor Warwick Davis (Willow, Leprechhaun, Harry Potter). Warwick Davis got famous in the Star Wars universe for his part as Ewok in “The Return Of The Jedi“. This scene is a little cameo. Too bad it was removed... source: Chris Ghould/DVDactive)
( 2 sec. )

0:53:57
A short dialogue between Anakin and his mother is missing. His mother tells him to take care. Anakin promises it.
( 12 sec. )

0:55:11
The pod racers get started.
( 6 sec. )

0:55:38
The turbines of the pod racers start running.
( 3 sec. )

0:55:43
The turbines get on.
( 13 sec. )

0:55:45
Another shot of the running turbines.
( 2 Sec. )

0:59:14
Shot of a tradesman.
( 5 Sec. )

0:59:19
The race goes on.
( 32 Sec. )

0:59:50
At Anakin´s racer the anchor of one of the engines breaks up and his racer turns around its own axis. Shot of the announcer: “Skywalker is spinning around. Uncontrolled!”
( 4 sec. )

0:59:53
Anakin get his pod racer under control again and manages to grip the chaining of the engine with the help of a magnet stick and reattaches it. The race goes on. One of the participators gets shot by the Tusken Raiders. (this scene is shown in the Theatrical Cut at 0:59:57)
( 53 sec. - 19 sec. = 34 sec. )

0:59:57
In the Theatrical Cut: the scene from 0:59:54 - The race goes on. One of the participators gets shot by the Tusken Raiders.
( 19 sec. already taken into account at 0:59:53)

1:16:06
Now there is a difference between the Theatrical Cut and the DVD Edition:

DVD Edition: Anakin turns to the two Jedis. The servant says that he should come with them now. Shot of Anakin and Jar Jar Binks in some kind of air cab. Several shots of them flying through the air.
( 45 sec. )

Theatrical Cut: You see a shot of a building in the city. The shot of Anakin and Jar Jar Binks stars earlier.
( 4 sec. )