Today's ride began with my discovery that the rear shifter couldn't hold the gears very well. Then my watter bottle, too heavy for the rusting-out bracket, dragged the bracket into my front gears, probably causing some damage as I was going along at a decent clip.
I got it to Bicycles Plus in Bedford and after a good-natured chuckle, the guy put my bike on the holder thing (you can tell I'm a bicycle expert), and he discovered that I'd bent a tooth in my largest front gear. He straightened that out, and then diagnosed that my rear-shifting problem was partly due to a very old cable and the general messy state of everything. He showed me that I could just turn the indexing off, which was a great work-around. I don't really need the indexing.
I'm going to hang onto this bike, because it'll be good to keep here for the times that I'm staying here and there's no bus service. But I still very much want a new bike and will start budgeting for one.