Ok, so I'm moving my research out of my question and placing it in an answer.
The joke here is that, while Indy is an accomplished "adventurer", he's not so good at being a professor -- at with least the clerical aspects of the job.
His secretary, Irene, says:
Dr. Jones, I'm SO glad you're back.
Your mail is on your desk. Here are
your phone messages. This is your
appointment schedule. And these term
papers *still* haven't been graded!
Back at school, Indy is immediately overwhelmed with paperwork. What's more, I looked at the original script, by Jeffrey Boam, and I discovered the following:
Students once again CLAMOR for his attention:
"Doctor Jones!" "Wait, Doctor Jones!" "My grade!" "My term paper!"
It's clear that Indy sees his job as a bit of a chore, and so actively avoids grading his students' work, or giving them the feedback they need. It seems he'd rather be adventuring and so neglects his duties as a member of staff at the college.
Instead of dealing with his irate students, he makes up a ridiculous scheme (whereby poor Irene has to try and decide who should be seen first) and then jumps out his office window.