It's probably a permissions problem. Even though some of your clips appear to be "read/write" there are probably other files in the project, maybe even the project file itself, that are secured to your MBP user account (because that's where you created them). When you copied the files from your external HD to your iMac's internal HD they carried their original permissions with them.
I don't know how important it is for you to preserve file/folder permissions on your external HD but if it's not a big deal to you, the simplest fix would be this:
1. Reattach the external HD to your MBP, log back in to the account you used when you set up your scratch disk location on your external HD.
Then, in the Finder, select the external HD, do File > Get Info, click Ownership & Permissions, then CHECK the box that says "Ignore permissions on this volume". Close the Get Info window.
Note: if you are going to move your projects back & forth between 2 Macs, you should use your external HD as the scratch disk location AND make sure "Ignore permissions on this volume" is set.
2. Then, with your external HD still connected to your MBP, use the Finder to select the Final Cut Express Documents folder on your external HD. Do File > Get Info, click Ownership & Permissions. Then set the permission for Others to "Read & Write" and click "Apply to enclosed items".
This will cause OSX to ignore permissions for all folders/files written to the drive in the future and will ensure that every file/folder in your Final Cut Express Documents folder is set to Read/Write for all users on any machine.
And btw - since you copied your files/folders to your iMac's internal HD before doing all this (above), you should get rid of those copies because they still have the old (original) permissions.