Every time I take a screenshot, I get this error:
You don't have permission to save files in the location where screen shots are stored.
How do I fix it?
If you type
defaults read com.apple.screencapture location into a Terminal window it should tell you where OSX is currently trying to save screenshots.
You can change the location with a similar command. For example:
defaults write com.apple.screencapture location ~/Desktop will save screenshots to your Desktop.
defaults write com.apple.screencapture location ~/Documents will save screenshots to your Documents folder.
Once you've told it a new location you need to run the following command for OSX to pick up the change.
Run disk utility and select your hard drive, then repair permissions. While you can do this with apps running it would probably run more smoothly and quickly if you quit out of all open apps before doing this.
If repair permissions fails for whatever reason start the Mac in recovery mode (COMMAND-R upon reboot) and then go into disk utility and repair the disk and then permissions.
If it still fails it may be time for a 3rd-party disk repair utility.
Another case where this error will occur is if the connection to a network-based home folder is broken. A bunch of other trouble will occur simultaneously, but if you try to take a screen shot of that trouble, you'll get this error message. (From first-hand experience)
Doubt that this is the answer to the original question; but it's probably worth noting nonetheless.
Make a new user and see if the problem is due to errors on your account would be my first step.
Once you know it's a system problem or a user problem you can proceed as the fix is different for both. I would start a new thread with this detail added since there are going to be two cases to solve for the general situation causing this error.
You could also use the Grab app to save the screen shot to a place you do have permissions and avoid the system screen shot problem entirely.