Hey checkin (btw, we use our real names here, please read forum rules),
The first thing I'd check would be the tape.
If you don't have access to a machine that's known to be running correctly, try some other tapes.
A tape machine's primary duty is to move the tape across the heads uniformly at the stated speed. So, almost all the mechanical workings of the machine are suspect when this isn't happening.
To make a guess over the internet about what may be happening with your machine (if it isn't the tape) we'd need to know the model of the machine and it's background.
My wild ass guess is that the tape you're listening to is curled.
Old tapes (particularly acetate backed) can become deformed if they aren't stored correctly.
One way to check if a tape is curled is to lay a foot or so on a clean flat surface. The tape should lay flat. If the edges are wavy the tape is curled.