The issue is that when opening the Git bash shell on a new installation of msysgit, the /etc/profile script (which runs at every login) tries to verify the MD5 hash of the main DLL. If it successfully validates the binary, it deletes the file containing the hash. If the file doesn't exist, it assumes the validation has already been done, and won't fuss about it. If it attempts to delete the file, but the user does not have permission, it will display a misleading error message: "ERROR: Your msys-1.0.dll is out-of-date!"

The directory into which Git is installed probably has permissions such that a regular user can't modify the installation. For example, "C:\Program Files (x64)\Git" is read/execute only for normal users. The solution is to manually delete the file using a command prompt with Administrator-level permission:

C:\>del "C:\Program Files (x86)\Git\etc\msys-1.0.dll.md5"

Incidentally, this is what the hash should be:

[jlamoree@STEWIE Git]$ md5sum bin/msys-1.0.dll

f3556c0fce4ca9a24fbdb78630afc47f *bin/msys-1.0.dll