Q: iMovie 10.0.2 shows that it has updated twice

Do you have any backup drives attached like a SuperDuper Clone or a Carbon Copy Cloner Clone? If so, OSX will see that version of iMovie and notice that it has not been updated yet. When you make the next clone, it will be all right.

In my case, it updated then said it needed to be updated again! No such Clone here. All native.

You might try going to Disk Utility and repairing permissions.

Same here on a MacBook AIr:

A real pain with the ADSL speed here in rural Spain!

Or, I could just wait until the OS X 10.9.2 Update is installed. The duplicate listing was removed after the update was complete.

Same problem here. It's really annoying. Any fix on this?