How can you tell if the shaft is bent on a lawn mover?

To do this you tip the mower on it's side on stable ground. Disconnect the spark plug lead and rotate the blade by hand whilst watching the shaft bolt. If the shaft is bent the bolt will move in a circle pattern.

To perform this test more accurately you need what's called a "dial indicator". A makeshift one would compose of a brick or any object that's 1/2 of the blade length. On top of that you place a pencil pointed to the edge of the shaft bolt. This gives you a reference point to watch while turning the blade.