When Zack and Miri get their name tags from Betz, Miri places her name tag a few inches from the top of the dress. However when it cuts back to them, her name tag is higher up and on an angle. Zack's name tag also changes position between shots.
When Zack tries to convince Delaney to be the producer on the escalator in the mall, the alternating close-up shots of Delaney and Zack show that they are already at the top of the escalator by the end of the conversation. However, when they show the shot of Delaney trying to decide before tossing Zack a bundle of money, they are still a few seconds away for the top.
When Zack and Miri come home from their high school reunion, Zac has a trophy in his hand. There is no reason explained in the DVD cut why he has a trophy. However, in the deleted scenes part of the DVD, there was a scene where Zac and Miri won a trophy for being the people who lived the closest to their high school as opposed to the trophy for people who moved the furthest away from their high school and it is pointed out Zac and Miri live across the street from their high school.
Zack and Miri are supposed to live in Monroeville, a suburb of Pittsburgh PA, yet right next to the coffee shop is a Hollywood Tans. Despite claims to the contrary, there are Hollywood Tans all over the US - including in Monroeville, PA.
The shots of the auditions were actually set in a playhouse that was originally a much longer scene that was meant for the full feature film. Due to time restraints the scene was cut out and just used as an internet trailer.
When Zack and Miri are in the coffee shop, Miri talking about she is unwilling to sleep with a stranger. You can see a coffee pot half filled with coffee. In one of the scenes (at the end of this shot) you can see the coffee vigorously shaking, as is its just been put on the coffee stand, but the seconds both previous and after to this it's completely stable. This happens because Zack had been leaning back against the counter and when he pushes off it jars the counter slightly and disturbs the coffee in the pot.
The goof item below may give away important plot points.
Towards the end when Delaney is showing Zack the footage of him and Miri, we see shots where the camera is pointing up at Zack from the ground. But they only had the one camera at a wide angle, and filmed the scene only one time, so they had no way of getting those shots.