I have the exact same problem on my MBA 2011, all started after upgraded to El Capitan, and seriously all that suggestion on resizing photos/exporting using highest resolution did not help me (and even if it would, why it started only after the upgrade?) And why should i be limited by those options? Shouldn't the application work for me not the other way around? Anyways I tried everything I could find on the support forum and to this day I am still hoping a new apple release update could fix the Mac OS/iMovie/ graphic card problem. To be honest I am surprise apple keep the MBA 2011 around this long (consider the iPhone4s from the same year is drop out from iOS 10)
And here is the end of the sad story, definitely not a suggestion (because I myself HATE this BS), but I bought a new MacBook in 2017 and it was able to export the movie in MP4 format using the same settings from the exact same Library on the exact same USB external drive and the movie came out normal. 😠 Hopefully I am the only person have to go thru this process, with this iMovie issue.