Try this. Connect a flash to the camera with a PC cord. Don't mount the flash in the shoe. Remove the lens, and use the flash to freeze the motion of the shutter curtains. At synch speed or below, there should be a clear film gate, and the mirror should be well tucked up. At speeds above the synch speed, there will be a slit - the higher the shutter speed, the narrower the slit. The slit width should stay uniform for a given speed, and you should still be able to see whether the mirror is out of the way. Don't look directly at the flash!
This isn't an infallible test, due to the very short duration of the flah, but it might show you something - such as shutter wierdness.