The File/Export menu was disabled many versions ago. Outputs now all found under Publish & Share.
If all you want to do is view it on the Mac, I'd recommend you use Publish & Share/Computer/AVCHD using the preset for either YouTube SD or YouTube HD (depending on whether you want an 855x480 or high-def 1920x1080 video). You'll be able to view this with Quicktime Player or, even better, with the excellent VLC Player ( a free download).
If you plan to do anything else with the file (ie, use it as source video in another project, use to to create a BluRay or DVD, use it on a Web Site) there may be a better optimized file. But, for just viewing on a computer, this Publish & Share option creates a very sharp MP4.
I would need more information about your Timeline content - especially frame size, frame rate, interlaced or progressive. You say it is a .mov file.
So for now, I will generalize....
Do you have the latest version of QuickTime installed on the computer with your Premiere Elements 10?
Share/Computer/Quicktime should be fine for a H.264.mov file export for viewing on Mac.
(Share/Computer/AVCHD might be a possibility for a AVCHD.mp4 file export for viewig on Mac)
Premiere Elements 7 was the last of the Premiere Elements versions to offer a section named Share as well as File Menu/Export/ with more than just the Export to Title. After version 7, there is a File Menu/Export, but it is only for saving titles created in the Titler.
Please let us know more details of your project settings so that we can fine tune the export suggestion with real numbers.
Add On...I did not see SG's post until after I had posted mine.
Just a reminder (a just in case add on)
a. once you have decided on the preset for your export under the choice of your Premiere Elements 10's Share/Computer/QuickTime or other, do not overlook the export settings customization that is possible under the Advance Button/Video Tab and Audio Tab of the selected preset.
b. if you need any help with the export settings, please do not hesitate to ask