Great info by many posters... I also seem to recall that the aircraft was not designed originally with an APU. Supposedly (and keep in mind that unless you verify this it's little more than aviation fokelore) by the time Boeing's marketing folks got feedback/requests for an APU from their 707 customers, Boeing was already well into the design phases of the 727. The wing root was the only place to install it, so there it went. To this day, **NOTHING** will get the lucky passenger's immediate and undivided attention as when the APU (the exhaust port being just outside his/her window) has the bad taste to "torch" on start-up or shutdown. Passenger-initiated evacuations have occurred from this...
If you'll do a google.com search for "727" you'll undoubtedly get hits for numerous sites by 727 junkies. I'm sure you can find lots of stuff there..
Some tidbits, just off the top of my head, that may jog the memory of others, and/or help your research....
1/ The stuff on the high sink-rate accidents in the early 1960s is a good point. I was a kid back in Cincinnati when AA lost theirs there, and I also recall the United accident at SLC (right there on the runway). I seem to recall another, TWA(?), also in CVG.
2/ 727's had a tendency to have forward lavs that leaked, and formed "blue ice". On at least 2 occasions (National, in the 70s, AA in the 80s), lav ice broke off at altitude and was subsequently ingested into the #3 engine, which obligingly seized and at that RPM torqued itself right off the airframe. Gave a whole new meaning to the phrase "we lost an engine..."
3/ National also had the distinction of putting one in Escambia Bay off Pensacola FL (PNS) one night. Very shallow water there, thanks to a nearby barge, only 2 passengers succumbed. The picture of the aircraft sitting partially submerged made this three-holer look like a bizzare organge and white submarine. One jokester penned in the caption "ah-ooga, ah-ooha, DIVE! DIVE!" on the news photo in our crew room.
4/ Let's not forget good old DB Cooper and his aerial half-gainer off the aft airstairs with $200,000 of Northwest (Orient's) moohlah. If your report will have multimedia clip(s), you can catch a recreation of the stunt in the opening of the movie "In Pursuit of DB Cooper" (..with Kathryn Harrod, hubba hubba, 2 thumbs up...)
5/ In the mid-1970s as South Vietnam was failing, a World Airways 727 undoubtedly set a world record for the number of passengers aboard. I vaguely recall it was a 727-100 with something like 180+ passengers aboard (including hanging off the still extended aft airstairs and unretracted landing gears).
6/ If you're interested, I've got some fire department footage of an EA 727 doing a night gear-up landing on 09R at MIA. Comes sliding right at the camera, stopping about 100' away, and almost certainly requiring a uniform change for the photographer.
Good choice of topics for your paper, as this bird has quite a history, and its ruggedness is awesome...
ALL views, opinions expressed are mine ONLY and are NOT representative of those shared by Southwest Airlines Co.