I think the practice of doing something like this is fairly relaxed as long as you aren't selling the office episodes as products or transferring video product.
Have you considered working with the teleplays from some of the funnier scenes and generating a script make feature where people can dial in their names and friends anc come out with a "screenplay" like the office episode?
Kind of like a mad lib but with the screenplays for the episodes?
If it were me I would go one further and then use the text to voice feature to get a "reading" of the new "scene".
also, maybe talk about ratings per show, how the characters changed from that show, and what things per episode were significant in later episodes.
for example, when Dwight Schroot undercover misses a big meeting to drive the timecards to payrolll to the New York office, it's pretty much indicated he is serious about her. i ALWAYS THOUGHT THIS was a very significant moment and it as undercut by the rest of the episode.
Dwight, the office dweeb who prides himself on being as job focused as Michael, misses a meeting to do Angela's job.
Make a quiz per episode and then link to the Youtubes with the answers.
ps does NBC live feed these episodes? i think so. Just link there.