Can Apple Watch activity tracking be thrown off by movement? If someone has a nervous habit, such as twirling their hair, drumming on the desk, etc, throughout the day, using the hand that the Apple Watch is worn on, can this throw off activity readings (and sitting/standing reminders, etc)?

One would assume that the watch double-checks things like this by measuring heart rate, etc, to be sure, but I'm wondering about the technical implementation.
Yes it can. Only exercise uses heart rate currently to gauge effort. I know of several people that figured out how to game the stand goal while flying in an airplane by just moving one forearm. 

The accelerometer algorithm for standing can't really tell why your hand moves when it is checking for sedentary conditions. This is probably a known issue since preventing this would also reduce the accuracy of legitimate walking about so it’s probably an engineering trade off as opposed to something Apple didn’t consider.