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Unfortunately, all the above posts have failed to recognize a KEY reason why it looks like this. You need to deinterlace your footage.
Your camera shoots in 60i, right? Yes, it does. This means it shoots 60 fields per second, or 60 half frames. 60 divided by 2 = 30, the standard 30 fps. However, if you don't deinterlace your footage in post, you can see the differences in the field lines, creating that wavy look you see in your footage when you pan horizontally (see the shot at around 50 seconds).
If Premiere elements is anything like Premiere Pro, you should be able to deinterlace by changing your export settings. When you go to export, you should be able to find a check box that gives you the option to deinterlace video. Check that box.
The reason it doesn't play like that in Premiere is because the program does it for you. If you open your file on Media Player/Quicktime or whatever as a raw file, you'll see the lines, because that program can't do it for you.
But besides that, I'm not sure what the deal is with your fisheye. Work on getting smoother pans with your crane.