My animation snaps in certain places. There's no key to snap to, or remove to prevent the snapping. I guess I could poke around in graph editor, but why is it happening at all? It's snapping in several different places, no matter the size of the movement. It happens on the first frame after a keyframe, then the rest of the frames move very slow until you reach the next keyframe, where it'll either move nicely, or keep snapping.
Check the graph editor. From experience it sounds like you may have two keyframes really close the each other that are causing snapping or you have keys where you didn't intend to put one (which is causing the slow movement and then snapping). You could also have keys set to stairstep instead of having smooth tangents.