Well, normally, pans like that are choppy. It’s an optical phenomenon sometimes called “judder”. The only way to avoid it is to change the motion from a simple pan to something more complex, to introduce distracting elements, or to use a faster frame rate or interlacing … and sometimes none of those are possible. But hey … feature films have the same problem, and it’s accepted.
HOWEVER … yours is worse than normal judder, and at low quality I don’t think normal judder is the issue in the case of your video. At low quality, you get what looks like pulldown jerk (stop it!) or something like that. This high/low quality issue may be a clue — it may be the player?
1) under what circumstances has it ever played properly? RAM preview in AE? QT export of AE-rendered Animation codec movie?
(I’d render a movie out of AE to the Animation or PNG codec, then use QT Player to export to H.264 Quicktime movie. Basically, change your workflow to try to isolate the cause.)
2) your judder is uneven. Something tells me that one of your compressing apps is making a 29.97 movie out of your material and messing it up. Or maybe it’s making a 15 fps movie, come to think of it. What is the frame rate of all the compressed movies, and what are the frame rate settings in your pipeline?