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)
Continuity mistake: In the beginning, after Dennis Quaid has been beaten up, the pins on his jacket are pinned, then hanging askew, then pinned again. (00:03:55)
Continuity mistake: Just after the scene where Jack Putter gets tazed by Lydia Maxwell in the restaurant, Mr. Igoe initially hauls the unconscious Putter over his left shoulder. In the following shot you'll notice that when he exits through the back door, he's carrying Putter over the right shoulder. This mistake was pointed out by the director (Joe Dante) himself on the commentary track of the DVD version. (00:58:10)
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.