Continuity mistake: At the end of the film when Kirk is being awarded his medal, behind the Federation Counsel you can see 3 flags in the background- the center flag is the California state flag. After Kirk shakes Pike's hand, and the camera pans up and back, the California flag is hanging significantly different so that it is no longer recognizable, seeming almost blank white. As the ceremony is indoors and all attending are standing motionless, this flag should not have moved. (01:56:25)
Other mistake: In the scene with the plane that is attacked by the mega shark and subsequently crashes, the camera focuses on one character in particular- a man who states he is "getting married in a few days". It is assumed when the plane crashes that everyone on board dies, yet in the very next scene this man walks behind Deborah Gibson's character as an extra.
Audio problem: Drake places the tea kettle on the stove having just finished pouring the water into his cup. The kettle whistle dies down as he places it on the unheated burner. The problem is that the whistling would've stopped soon after lifting the kettle from the hot burner, and certainly wouldn't have gone on while he was pouring. (00:57:10)
Factual error: The license plate on the sheriff's car when he arrives at the factory is 5Q49926. In California - where the film seems to take place - that is a "Commercial" license plate issued to trucks and commercial vehicles, but law enforcement are issued "Exempt" plates which are 7 numbers.
Other mistake: When Wes is running from the bad guys he hides in a St Patrick's day parade. No buildings that they pass have any St Patrick's day decorations or give any hint of this holiday, including the Irish bar they go into earlier.
Continuity mistake: When Maynard is teaching Tony to shoot a gun, Tony fires three shots first. The gun's chamber closes as usual (meaning the gun still has ammo). We see a shot of Maynard, then flick back to Tony and the chamber is now open (meaning the gun is out of ammo). Tony then fires three more shots from an apparently empty magazine before being told to reload. (01:26:40)