You May Now Kiss The...Uh...Guy Who Receives - S4-E25
Other mistake: When Peter is eating the Brownie, it stays the same with no bites.
Road to the Multiverse - S8-E1
Other mistake: In every universe - except for the double-headed universe - Brian and Stewie travel to, they (seem to) replace the version of themselves that universe already has of them, but then in the Dog universe they have a separate version of themselves that they continuously interact with.
Boys Do Cry - S5-E15
Other mistake: Towards the very end, they automatically head to the car, planning to leave Texas, without any of their items from the house packed in the car after running away from the mob at the Miss Pageant Contest.
A Picture Is Worth 1,000 Bucks - S2-E11
Other mistake: Brian says he met Antonio Monatti when he was with Andy Warhol in the '70s. This is an impossibility. Only several episodes earlier (in episode Brian in Love), we find out that Brian is 7 years old.
Blue Harvest - S6-E1
Other mistake: In the scene where the Millennium Falcon has just left the death star after Obi-Wan has been killed, there are two shots of the ship flying away through space. In the second shot, the cockpit is missing. (00:33:35)
Airport '07 - S5-E12
Other mistake: As Quagmire sits at the bar, Hugh Hefner comes and gives him a pep talk. During it, he says John Holmes said Glen Quagmire is the best pilot. Unless he had seen the news or knew him personally, Hefner couldn't have called Quagmire by name.