Hi,
Thanks for the reply! Good to know that the damage has been done and won't continue.
I wouldn't write off the possibility of further damages this easy.
Consider the case (similar to some ESD damages), where some components are weakened but not totally killed off, say by having a semiconductor trace partially blown. Next time it's asked to perform to specs, it may blow or be weakened further.
Depending on where the damage is, future issues could be a possible scenario.
Any pro would toss the complete PCB, sensors and chips and start over with new bits and pieces, as that is the only way to be sure.
That said, when you're on a hobby budget and you're not selling the finished board, the range of consequences will be fairly limited, should something break down, so I'd advice you to keep going, but to be sure, stock up what's needed for a new board JIC.
How about the battery though? What happens to the battery if it is hooked up backwards? How can I tell if it's been damaged? Does it matter as long as the voltage appears to be normal?
The worst possible damage that can happen to a battery from reverse connecting it (besides high current drain and possible fire, especially if using unprotected lithium based cells), is reverse poling (of one or more cells). This will weaken the cell(s) in question, even if it can be somewhat restored.
If you measured the nominal voltage right after removing the battery, this have not happened (would take more than a few seconds anyway).
Here's a way to protect against polarity reversals (you need a fuse anyway, so it'll just cost you a single diode)...
If you reverse the battery, the fuse blows to indicate that you F'd up
(1A fuse shown, but use whatever suits the circuit that you need to protect).