How can I tell if the fans are operating correctly on my MacBook Pro 17" (2010)? My Mid-2010 17" MBP seems to be running warmer than normal recently; I've read that fan failure is not unheard of on systems of this age, but I don't know how to verify whether one or both fans is operating correctly.

I have removed the cover and checked that there is no obvious buildup of lint, etc., in the fans and they spin freely.
You can use the freeware application Macs Fan Control to monitor both your current fan speed and your internal temperature. It also allows you to set a minimum speed for your fan(s), which you could use for stress testing your fans by temporarily jacking up the speed, or for permanently increasing the minimum fan speed somewhat if you feel like your Mac is running a little too hot.

It also has a diagnostics mode, which I haven't used yet, but which could be useful in your situation.