This isn't really a FCP tip per se, but I was editing -doing a favor which is another way to spell free- at someone's home recently helping them with a project and noticed after a while that their Time Machine back ups were taking forever; it seemed to be constantly running. It was using a bit of CPU and really thrashing a connected drive.
I checked the Console (Applications > Utilities > Console) and typed in "Starting standard backup" into the search box and looked at the times Time Machine had been running. Looking at the times between "Backup completed successfully" and "Starting standard backup" I saw that backups were taking near 50mins, meaning that Time Machine wasn't grinding away for only 10mins every hour.
I looked around a little bit and one thing to try to fix this, other than just turning it off as it's a problem from 10.6.x all the way to 10.8.x, is to perform a Safe Boot.
1. Reboot the Mac
2. Right after the Startup Chime (Bong noise) hold down the SHIFT key, this is called a Safe Boot
3. Wait for a while. You may see not only an Apple logo on the screen above a "Gear" wheel but below that you may see a progress bar as well. Keep holding down the SHIFT key
4. When it finishes booting (and log in if it asks you to) wait for it to settle down, don't launch any apps, then Reboot. This time don't hold down the SHIFT key.
5. Wait for Time Machine to run again or force it to run by selecting it from the menubar and selecting "Back Up Now"
In a backup or two you should see back ups moving along much faster. There's some complicated stuff going on here with UUID's and Deep Traversal but this is one quick thing to try to solve it before you delve into deleting backups or using another drive (which people often think fixes it but just starts a new backup which you could get by formatting your current Time Machine drive) or running repair utilities.
This process is for if you have a Time Machine back up drive directly connected to a Mac. I'm not sure how well or if at all, this would help a slow network backup.