What kind of camcorder did your video come from and how did you get it into your computer? There are dozens of types of MOVs, only a few of which are supported by the program.
When you set up your Premiere Elements project, which project settings did you select?
Have you ensured that you've got the latest version of Quicktime, per the program's requirements, from Apple.com?
If you're looking for some basic how-tos for using the program as well as information on how to properly set up a project, checck out my free 8-part Basic Training tutorials at Premiere Elements support site Muvipix.com.
Welcome to the forum.
As Steve points out, MOV is but a "wrapper," and it is what's inside, that matters. The same holds true for AVI's, WMV's, and more. This ARTICLE goes into more detail.
When one begins a Project, at New Project, they need to know the details of their Source Files, and the Project's Preset, chosen at New Project, must match that Source Footage. That is why it is so important to know about that footage - so one can match to it. If you will tell us all about that footage, someone can help you make sure that your Project Preset matches, so that you do not have issues.
With playability issues, the first issue is the match between your Project Preset, and your Source Footage. Next comes one's system, so it might be a good idea to start gathering up the info there. This ARTICLE will give you some ideas on what infot would be so useful.
You may need to invert the field order. Right-click the clip on the timeline, choose Field Options, and check Reverse Field Dominance.
This suggestion is made presuming that you are viewing your output on a TV set which is not capable of progressive scan. To explain, TV transmissions did not send a full frame each time, but half-frames, alternating odd- and even-numbered lines on the TV. Video files followed this same format, with interleaved half-frames. Latest systems use progressive mode, with full frames every time. If you're dealing with interleaved frames, there is a possibility that PE is outputting the half-frames in the wrong order, which means that the motion will be out of synch and the result is visually disturbing. Inverting the field dominance will get the half-frames in the right order.