Gretchen being class president is never brought up again in the series.
This episode is one of only two that credits Etan Cohen as a writer; the other being the episode "The Rules." However, on both of these episodes he did co-write.
This is one of only six episodes of the television show Recess that were directed by both Sheetz and Parkins, the two prominent directors of the series.
It's unknown why Vince and Gretchen had to convince the entire playground to vote for one of them. One of them would only be president of their classroom, so there would be no reason why kids from other classes or grades should vote for them.
Gretchen should have won by two votes if all boys (except Vince, Gus, and Mikey) voted for Vince and all girls voted for Gretchen, with it being stated there were two more boys than girls in class. Assuming twelve boys and ten girls in the class with Mikey and Gus abstaining, that's ten votes for Vince and ten votes for Gretchen, making it a tie. Vince decided to vote instead for Gretchen, giving him one less, and Gretchen one more making it Vince nine to Gretchen eleven.