Electrical – Unknown rubber piece on electrical box

If wires spark enough to generate a burning smell, you'll hear the arc and it's also possible the breaker would go as well.

From the symptoms you describe it sounds like the dimmer itself is going. Since it has a burning smell, I would say it's unsafe to use and you should replace it immediately.

Of course, if you see any nicked wires, or any of the wire nuts are loose then you should fix those problems. Be sure to turn off the power at the panel when you're doing this (you should check with a non-contact voltage detector just to be safe).

My approach (not an electrician, just a guy with a meter) would be to start by mapping the circuit (find all of the outlets and fixtures that are on it), then unplugging EVERYTHING that's plugged into that circuit and see if that has an effect.

Next up, I'd kill the breaker and open up the switches and take a look. See if there's evidence of burning or arcing, or if one switch feels different than the other. I'd probably disconnect both switches (safely capping all wires), then turn the breaker back on and verify (using a meter) that the voltage is reasonable at all the outlets and other fixtures, and see what happens in the bedroom.

Basically if that tells you nothing, then I'd either start pulling outlets and fixtures off the circuit (kill breaker, remove outlet, capping wires, breaker back on) until I figured out what the heck was wrong, OR I'd just call an electrician.