when I lunch Cheese Webcam Booth this is what the picture looks like
and it keeps changing between these 2 colors every 0.25 sec
I recommend going to Preferences -> Image and changing the Hue level. Simply changing it should set a value to it (In the case there is no default value set). You should know that Cheese has some problems that could come back from one version to another. This is why I have a backup like Kamerka
or Kamoso
which are found in the Software Center and do not suffer from several Cheese related issues.
Another factor that could cause this is the resolution. Try changing the Cheese resolution to one smaller/bigger and see how it behaves.
If changing the Hue or changing the resolution does not solve the issue file a bug report and try to use one of the other recommended meanwhile.
Do you happen to use any Effects by mistake (bottom right button)? Have you tried to differently lighted room (lighter or darker)?