Well, I got it wired up and started to check it over. I ran a cycle with no clothes, and it worked fine up until the rinse cycle, where it would get stuck and keep turning indefinitely. I figured out that a couple taps on the timer with a small hammer were enough to get it to advance, so it will need a timer rebuild or replacement. I figured as much, so I was happy that all the other functions were working.
Now, for the part that most of you already anticipated...
The former owner said that he had it LOOSE on the floor, NOT bolted. Myself, being naive, believed him, though the bottom frame has a set of nice mounting holes that must have been for something? The test run seemed to support his statement, as the machine didn't even start to vibrate on the spin cycle. So, I put together a load of old towels and clothes to try it out for real, and when it hit the spin cycle...
I couldn't hit that OFF button quickly enough! It shook, rattled, rocked, and leapt 6" off the floor. After I cut the power, it still shook like crazy for a good 20 seconds until the drum came to a stop. So, I'm off to borrow a concrete drill and some bolts...