Im getting a message that a the disk is a full and cant save anymore. Im trying to change the directory but to no avail. It says it's invalid directory.

Which game are you having the problem with? Also is the drive you are trying to save to actually full?

If you're on Windows 7/Vista, run the game as an administrator.
The message could also means that the game is unable to create a save due to OS restricting access to Program Files folder.

DOSBox has this issue with old Sierra titles when you install them into the %Program Files% directory. Uninstall the game and reinstall it to the root of your hard drive.

ex. instead of: C:\Program Files\GOG.com\Police Quest Collection\

try: C:\GOG.com\Police Quest Collection\

Because DOSBox has the game's directory mounted as C:\ you cannot change the save directory in-game.

this is not dosbox it's problem.
It's windows that forbids the writing on stuff in c:\program files

These Sierra titles are the only ones I know that have difficulty saving in the %Program Files% directory with DOSBox, all my other GOGs that use DOSBox can save there just fine. But yeah, Windows restricts access to that directory for safety reasons. All the same, it's an easy fix.

Windows behaves differently (in what it allows in program files) based on the extension of the file that is being saved. I did a lot of research on this as I wondered why certain games had no problems and others wouldn't even run (as I wondered if we (dosbox team) did something wrong).
I should one day make a huge post about it explaining all the different behaviours.

GOG needs to either install to \Games or modify the NTFS permissions for "Authenticated Users" if they insist on installing these old games into \Program Files.