Yes, it could be the switch. The switch should disengage after the motor reaches a predetermined RPM range. It's usually underneath the bell guard in the back of the motor. Although this is a common problem with cheaper Asian motors, good compressor motors should not be prone to that happening.
The contacts have a tendency to stick and pit as in old point type distributors. Hence. they can slightly "weld" themselves together and not separate. If they are stuck, you can try resurfacing them with emory cloth, or an ignition point file.
As far as the capacitor is concerned, your nose is the best first diagnostic. If you smell anything burnt, then you found the trouble. To test the capacitor further you need an Ohm meter. Unfortunately, with an Ohm meter doing an "incircuit test" is not very accurate (you'd need a capacitor tester for that). So you might have to disconnect the the capacitor from the circuit to perform a proper test.
Make sure you discharge the cap first though -- the proper way to that is to use a jumper wire with a 10K ohm resistor in the circuit. Although not recommended, some simply bridge the connections with a screw driver -- this may cause a good spark!
Once it's discharged, hook an ohm meter to both sides and watch the meter. A good capacitor will show no resistance (0 ohms) at first, and gradually build up resistance as it charges (using your meter's battery as a power source). If the meter just shows infinite resistance, or no resistance at all -- then the cap is probably bad.
EDIT: Or take Toolman's advice -- he's probably the authority on this. Experience is the key here.
