Plot hole: They're in the Clam complaining that they can't drink when they make the revelation that Brian can because he's technically 56. But Quagmire should be able to drink, as in a much earlier episode, he's revealed to be over 60.
Other mistake: When Quagmire is sticking his body out of the car door and yelling "Whooooooa! Whoooooooa!", look at the person in the back seat. It certainly isn't Joe, who was there in the previous shot, in fact it looks like another Quagmire. (00:05:30)
Continuity mistake: When Mr. Weed is crying about losing his job, we see a view of a long line of trees in the window behind him. The camera switches to a close-up of Peter. When it zooms out again, the trees on the right of Mr. Weed are missing.
Revealing mistake: When Brian says "Well face it Peter, your attitude towards women isn't exactly enlightened", Brian's dog tag is the same color as his fur. It also stays still, even while Brian is moving his head. (00:11:10)
Plot hole: Brian and Peter see Loretta and Quagmire having sex yet, they aren't sure who she's having an affair with. There's no way they couldn't have noticed it was Quagmire - the couch was facing the front door! And obviously Quagmire was on top of Loretta considering the fact that he leans up, says something, then she tells him to get back down here and finish.
Factual error: Joe's plan to trick OJ into confessing to the 1994 murders is moot since, having been acquitted, the double jeopardy provision would prevent him from being tried for the same crime twice, and as a cop, Joe would know that.