Try booting up in Safe Mode and, after everything loads, immediately shut down and reboot in normal mode. That might clear out any conflicts that might be causing the sharing out failures.
If Safe Mode doesn't work, try redownloading iMovie 10. To update/redownload iMovie 10, drag your iMovie 10 app from the Applications folder into the trash, but do not empty the trash. Sign in to the app store and open your purchases folder by clicking on your name at the bottom of the app store side bar. You will see your purchases displayed, including iMovie 10.
Redownload/update iMovie from there. If not successful, drag your present iMovie app out of the trash and return it to the
Applications folder.
If still no luck, try re-encoding the clips in the movie with the free download, Handbrake, to H.264, Mp4/AAC (even if it is already that format). Handbrake will re-encode the clip to that format by default. To begin, put your clip on your desktop. Then open Handbrake and do a File/Open Source. Navigate to the desk top display of files. Double click on your video clip to choose it. Then do File/Start Encoding. After the clip is encoded, drag it into iMovie and see if you can share out.
-- Rich