Jack tells Carl he's the new sheriff and it was announced at a "Town Meeting". Actually, the town meeting sequence had not been aired yet. The episodes were shown out of sequence in an attempt to load the stronger ones first to bolster ratings.
The physiological monitoring device Allison attaches to Carter's neck at the beginning of the episode is not seen in several scenes thereafter.
In his lab, Dr. Carlson explains to Sheriff Carter how he is working on cellular regeneration, and cites as an example how lizards are able to regrow their tails if lost in an accident, etc. As he talks, he gestures towards a tank with a lizard in it. However, in the tank is a chameleon, which is actually one of the few lizard species that does not possess the aforementioned cellular regeneration characteristic, and is unable to regrow its tail.
Jo has an Oregon flag and a US flag behind her desk. The US flag is to her left as she is sitting down. It should be on her right. The US flag is always displayed on the right as it has precedence over any other flag.
During the Carlson bridge scene, Carter climbs over the railing to join him. You can notice that the bridge is concrete, but when he climbs over, the bridge is made of plastic and wobbling.
There is a conspicuous gap under the supposedly radiation-proof blast door in Section 5.