Factual errors: The final screen of end credits for each episode contains a standard disclaimer about all characters being fictitious. In the second season episodes, this is misspelled "ficticious".
Revealing mistakes: The most frequent animation error seen in the show is the appearance of the eyebrows (and some cases the eyes). The eyebrows are known to disappear and/or reappear at times, or in rare cases even "duplicate", creating an extra pair of eyebrows (as seen on Lois' father when Peter meets him in "Death Lives").
Continuity: When Lois is in jail following her stealing spree, she's wearing her standard yellow prison garb. When Peter sticks her in his mouth to smuggle her out, she's back to her normal clothes.
Continuity: When Joe discovers the Griffins hiding out in Asiantown, Peter switches between his sumo outfit and his regular clothes.
Continuity: In "No Chris Left Behind", the Morningwood Academy sign has "NO IRISH" crossed out and "IRISH OK" written under it. The next time we see the sign, there is no trace whatsoever of either line of the Irish text.
Continuity: In certain episodes, the floor in the upstairs hallway changes from hardwood, to carpet, then back again.