It's difficult to make out what exactly is wrong, but if you're referring to the colours being all screwy, it's probably the famed DirectDraw colour palette problem. If it's happening in DOSBox, you probably have your DOSBox screen settings set to "ddraw".

In DOSBox, change this to "opengl" or "direct3d".

With Windows games, there's a variety of solutions, most of which involve creating a batch file which kills EXPLORER.EXE while the game is running. I personally use Seppe vanden Broucke's excellent Palettestealersuspender (http://blog.macuyiko.com/p/palettestealersuspender.html) as a more elegant solution.

On a side note, does this behaviour occur in Windows 8 as well? I can't really replicate it properly in a virtual machine...

A permanent solution to this would be to edit the .conf file (you can check what the .conf file is named if you right click on the shortcut->properties. In the box named "target" you will find a place where it says -conf "name of conf file".conf
like this:
"C:\spel\Master Of Magic\DOSBOX\dosbox.exe" -conf dosboxMOM.conf -noconsole -c "exit"

Go to where you've installed the game and find the conf file. Open it in notepad, and look for a line that says output="method of output" (it should be relatively near the top of the document, but just search for "output=" and you should be able to find it). Change whatever it says to opengl or direct3d (or if you are feeling adventurous, something else. The other supported output modes are: surface, overlay, openglnb, ddraw)

If you're not using a GOG version, then yes, that is the only solution.

The GOG configuration program will automatically modify the .conf file, if that's what you're getting at.

*chuckles* Silly me never even thought of the GOG "graphics mode setup" up until now :P I'm so used to working with dosbox that whenever I've had a problem with a GOG release, I've just edited the conf file :P

I used to use a batch file to kill explorer until I found this Direct Draw Fix program that solves the problem without killing explorer. It's the best solution I've found. http://www.xomicron.com/software/directdrawfix/