The episode's Dean Peterson doesn't seem to be the same Dean Peterson that Homer ran over during a prank in "Homer Goes to College", although the security guards' dialogue implies that he is. It's possible, though, that the stress of work had jaded Peterson and aged him considerably in just a few years.
Homer sings "Aloha 'Oe" two episodes in a row. In "Little Big Mom" he sings it while undergoing treatment in the electric needle hut. In this episode, he sings it while showing Lisa his animated drawings of Moe doing the hula in a grass skirt (however, this time it's actually "Aloha Moe").
The episode title could refer to a sports face-off, or 1997 action movie Face/Off.
When the bucket falls on Homer's head, he's wearing a hat. The bucket should have slipped off stuck to the hat, not Homer's head, without the need for pulling. When the bucket is removed, the hat seems to be no longer there.
During the end of the song Testify, there are three close-up shots on Bart. During the second close-up, Bart is wearing his cape but in the next shot, he is not.
Why didn't Hibbert just get Homer to sweat out of fear, like he did in "Lost Our Lisa"? Homer was unable to see until Bart drilled in the eyeholes, so he couldn't see anything potentially scary.
The fork that got stuck in Milhouse's cast is only seen when the camera zooms in to show ants going into it.
When Brother Faith says "But that's not God's angle!" his eyebrows disappears.