Have exact same problem.
I just purchased a 2006 325i yesterday with the exact same problem. Worked fine during about a 30 minute test drive. By the time I got the car home (about an hour drive), the display was completely unintelligible.
Drove it 3 times today... when the engine and car are cold, the display is fine, after about 30 minutes of driving, some parts get darker, the longer I drive the worse it gets.
Don't have an answer yet, if you come up with something, please let me know, too.
If I get an answer, I'll post it for you here.