Welcome to the Support Communities!
Are you working on your internal Macintosh HD or are you using an external drive for your iMovie projects?
Do you have your data backed up via Time Machine or some other means?
You can use the Finder application to "Get Info" on the internal or external drive to check the capacity, and amount of free space available.
You should also review the "Sharing & Permissions" settings for the drive.
Disk Utility can be used to check either drive for permissions issues.
The following artilces may help you with this:
1. Click the Finder icon in the Dock.
2. Select an item in the Finder (ex. Macintosh HD or your external drive)
3. Choose Get Info from the File menu (or press Command I)
I hope this information helps ....
Have a great day!
I have had this issue before as well with my original setup (2011 MBP 17", OSX Lion) and I had over 100 GB of storage still available at the time. I believe before that on the all the steps up the file tree leading to imovie library I selectedr: get info > sharing & permissions, I changed myself to read only and then back to read & write. Also I deleted some older projects and this seemed to remedy the situation for a while. But would still happen intermittently.
Recently, I've upgraded and added a second 500 GB internal HDD for video editing / storage the problem came back. Tried the previous methods to no avail. This time I used disk utility to unmount and remount the second drive and that seemed to do the trick.
Hope this is a more permanent solution, but I wouldn't be surprised if this issue came back again as this has been one of the more persistent, yet random bugs I've experienced on OSX. One only hopes this will be sorted in Yosemite... Guess I can't complain as it's all free. However it looks like a few people are having the same issue with Final Cut Pro.