Continuity mistake: When the fire truck swerves out of the way to keep from hitting a car, and tips over onto its side, we see it precariously balanced on two wheels. When they show a shot of the inside of the fire truck, we see that the fire truck is scraping against the ground. The side scraping against the ground is the driver's side, while the truck rolled onto the passenger side. Then in the next shot we see the fire truck still balanced on two wheels and then it tips and falls onto its side.
Continuity mistake: During Brian's graduation drink the bartender hands him a beer whilst ridiculing him about his numerous failed career moves. When the beer is poured it is about two thirds froth but as it cuts to another scene there is only an inch or so. Sufficient time has not elapsed for the froth to die down as it only spans one sentence of the bartender's dialogue.