I have one of those cheapy little timers that use the little pegs to trip it on and off. I think it is turning backwards. Can the polarity affect this or is it shot?
With respect to such devices, AC power has no polarity. The "polarity" is in the premises wiring standards. If your device is running backward, the starting method on the synchronous motor has gone haywire. I have no idea how to repair it. Buy a new one.
... not necessarily "haywire", so much as catatonic.
Most of those little motors will run either direction once started that way. If the starting arrangement fails to work at all, it'll just run whatever way it feels like.
The least-involved solution is to unplug it and plug it back in, hoping it'll start the correct direction this time. Of course, there's a 50/50 chance it won't, and the visible motion of a timer is so slow it'll take hours to determine whether or not it did.
If there's a way you can manually exert some force on some part of the timer that spins in use, do so in the correct direction while plugging it in. This'll at least increase your chances.
Or, as bus_driver proposes, buy a new timer.