When Bart and Lisa tumble into the creek, you can tell its pretty deep from the underwater shot of them choking each other. But when they resurface they're able to stand and the water's only waist deep.
On the field trip memorial wall when Willie has to enter Bart and Lisa's names, you'll notice two particular names. El Jefe (Hefe) and Fat Mike - horns/guitar/backup vocals and bass/lead vocals/founding member (respectively) of the punk band NOFX.
Bart's fanny says "Lisa's Brother" and Lisa's says "Bart's Sister."
After Lisa is given her paper, you can clearly see that there is a B+ on top of the stack of the papers the teacher is holding. But a moment later, she gives Bart an A!
Principal Skinner breaks the fourth wall in this episode, saying "If this episode has taught us anything...".
The song that "MC Safety and the Caution Crew" sing has a similar rhythm (possibly sampled) as Sugarhill Gang's "Rappers Delight".