Yep use a throwaway roll to verify the camera's film transport works. I've seen advances where the first frame or so works but then slipping or ratchet failing starts happening as the slack is taken out of the roll. This is with cameras that have a clutch like (maybe not literally, but *like*) advance spindle for when it needs to be rewound.
If its a camera issue I bet it coincides with when the roll has the slack taken out and the advance has to do real work.
Stop worrying about grain, resolution, sharpness, and everything else that doesn't have a damn thing to do with substance.