The first few times Tuck tries to talk to Jack (having placed his equipment in Jack's left ear, as suggested by the itch Jack feels and confirmed when the doctor shines a light in it), he tends to respond as if the voice is coming from his right.
When Jack looks in the mirror to make his face visible on Tuck's monitor, the resulting image should be "flipped" to represent his reflection. When compared to his non-reflected image, the part in Jack's hair never changes sides.
When Ozzie staggers out of the elevator and injects the pod into Jack, the needle enters in the middle of his left buttock, through his pants. However, when Dr. Canker is reviewing what are presumably security camera photos from the mall, Jack is shown being injected very high on his left buttock (almost into his lower back), and through the waistband of his jacket.
While the man and woman are shrunk to half size and trying to use a phone booth, the sky behind the booth changes in every shot. It goes from blue with distinct clouds, to grayish and cloudless, to a mixture of both and back again.
During the car chase with the little people, the car at one point is heading towards a concessions stand by the beach. Jack yanks the wheel and they perform a screeching right turn. In the next shot out of the front window, they are still heading toward the concessions stand.
When the two Pods battle in Jack's throat, the 'bad guy' pulls the power cables out of the 'hero pod's thrusters, disabling the pod. Then when the pod falls into Jack's throat, you see it impact the sphincter which leads into the stomach. If you look closely, you can see that the power cables are still connected to the engine, and they stay there until the pod is re-enlarged, when the cables are mysteriously detached again (obviously a continuity problem between the model and the full-scale mock-up).
The movie depicts miniaturization as, effectively, blowing up a full-sized submersible pod and then reassembling it at a smaller scale. There are several problems with this idea: 1) the pod would weigh just as much as before, and would therefore punch a hole right through the subject it is injected into because all that weight would be concentrated in a spot the size of a blood cell, 2) the Heisenburg Uncertainty Principle basically states that an object taken apart at the subatomic level would be impossible to reassemble, 3) Tuck would have died from being "molecularly isolated and displaced", 4) fluids would be impossible for a submersible to maneuver through because, at that scale, ordinary water would be like a gel to a thruster (not to mention bodily fluids which are thicker), and 5) whiskey would be impossible to drink.
Tuck's mini computer keyboard has a slightly altered QWERTY layout. "Z" is found to the right of "L" and under "P" - which arguably may not be a goof even if it would make typing difficult - but the bottom row reverses the usual placement of "V" and "C" as well, which has to be purely a mistake.