There is no problem to be fixed. The 20" iMac is absolutely capable of displaying "millions of colors" by using a technique called "temporal dithering". The 24" iMac uses a different display that is also capable of displaying "millions of colors" and may have a better quality for its higher price. You get what you pay for, and you pay for what you get.
Before you buy any monitor, whether standalone or as part of an iMac, you should go to a store where you can look at it in real life, and decide for yourself whether you are happy with the quality or not. If you are happy with it, buy it. If you are not happy with it, don't.