(at around 54 mins) 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.
(at around 26 mins) 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 (at around 35 mins), Jack is shown being injected very high on his left buttock (almost into his lower back), and through the waistband of his jacket.
(at around 23 mins) When Ozzy is being chased on the bicycle he passes the same yellow Volvo station wagon twice.
(at around 1h 45 mins) 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.
(at around 51 mins) After Jack takes the drink of Southern Comfort to fill Tuck's flask, the flask is obviously dripping wet on the outside of the pod but suddenly bone dry when he retrieves it.
Tuck should not have been able to see Jack's entire eyeball from the eye socket.
(at around 2 mins) Although Tuck is a Navy pilot, in the opening scene he is wearing Naval Flight Officer (navigator) insignia rather than pilot's wings.
When Scrimshaw and Canker are partially shrunk, their voices are slightly higher in pitch, just as a shorter person's would be; but Tuck's voice is normal the entire time he is miniaturized.
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.
(at around 1h 18 mins) When Tuck is reading the manual on how to manipulate Jack's face to look like the Cowboy, he is wearing glasses. Pilots have to have perfect eyesight.
(at around 55 mins) When Jack turns away from the mirror the picture in Tuck's pod should have turned with Jack's head, instead it stayed looking at Jack in the mirror.
(at around 1h 35 mins) The pistol that Lydia uses to free Jack is an automatic. When she fired the last shot the slide should have stayed back indicating it was out of ammo. She would have know this before they entered the stairway.
(at around 1h 40 mins) In the fight in the car, with the half-sized people, Scrimshaw's arms are way too long.
(at around 40 mins) Jack only presses buttons on the bottom of his TV remote, where power is unlikely to be placed, yet the TV turns on.
(at around 1h 21 mins) Even though neither Lydia nor Jack know that Tuck is capable of altering Jack's face to make him resemble "The Cowboy", for some reason Lydia has a fake gold tooth ready and waiting for Jack to wear.
(at around 1h 19 mins) When Tuck alters Jack's face and transforms him into The Cowboy, Jack's eyes change from blue to brown as The Cowboy has brown eyes.
(at around 24 mins) A boom mic is reflected in the car window when Mr. Igoe parks in front of the mall.
(at around 49 mins) Tuck says that the car is a 5-speed stick. Later it is an automatic.
(at around 21 mins) Ozzie refers to Bugs, the rabbit, as a rodent. Rabbits are lagomorphs.
(at around 37 mins) 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.
(at around 24 mins) When Mr. Igoe leaves his BMW to follow Ozzie into the mall, he prepares his "stiff" right hand. While he's doing that, you can clearly see that he his stretching his fingers...