Normally the phrase teacher's pet means
a favorite student. Here it is used ironically since the teacher herself
is an insect which could be kept as a pet.
Buffy: Well the words "bug
ugly" come to mind.
A twist on the slang expression butt ugly that is specially tailored
to an insect.
Blayne: I think it's eeny,
meeny, miney...
Xander: Moe?
Eeny, meeny, miney, moe is one of the
many childhood methods of choosing among various people. The nonsense
phrases come in various varieties with various lengths, but the basic idea
is that you point to a different person for each word and the person pointed
to on the last word is chosen.
Blayne: Flag down
on that play, babe.
An illusion to American football where the officials call a penalty
by throwing a flag. It's common to hear an announcer say "there's
a flag down on the play" to indicate that
a penalty will be called. Here Blayne is trying to deflect the information
that he's a virgin.