Revealing mistake: When Jack is hanging out of the truck you can see him standing on the hood of the car which Lydia is driving. At some points we get camera view from the back seat of the car. In some angles the mirror inside the car disappear. This is to prevent us from seeing the camera. (01:04:15)
Revealing mistake: When Martin Short is escaping the lab in Dennis Quaid's car, Dennis says that it is a 5-speed manual transmission. Immediately after this you can hear the car very smoothly shift up gears but Martin's hands haven't left the steering wheel. (00:49:45)
Revealing mistake: In the scene where Jack and Lydia are driving and the miniaturized Drs. Scrimshaw and Margaret are fighting them in the front seat, the washer fluid is spraying on the windshield, but it's not being blown around by the wind at all (indicating the car is stationary in front of a blue/green screen). A few seconds later, the scene cuts to Lydia and back to Jack and the washer fluid is off and the windshield is dry. (01:42:35)
Answer: Probably, but most likely it's because Jack's pod is fragile and wouldn't survive the shock wave heartbeats. The pod is experimental and built for scientific observation, not battle.