the short answer is: nothing will happen. The difference between the two is that DOT 4 has a higher boiling point, so you will not be as likely to have your brakes fade due to overheating in racing (open track or auto-x) or mountain driving. if you overheat the fluid and it boils, air bubbles will form in the lines, causing brake fade (squishy pedal) and in extreme cases your brakes might fail completely. DOT 3 and DOT 4 are both made with the same base fluid, but there are additives in the 4 that raise the boiling point.
Although mixing the two should not cause any adverse effects, it is generally reccomended that you dont mix the two. I have DOT 4 in mine with no probs. When i put it in, i pushed about three bottles through to make sure all of the DOT 3 was out.
there is also DOT 5, which is basically reserved for full race use, and it CAN NOT be mixed with DOT 3 or 4, as it is a different base fluid (silicone base i think). you would probably have to change out most of the components, or at least to a complete system flush to use it.
If you are not auto-xing on a regular basis, then dont even worry about it. DOT 3 will be fine for 90% of us.
Whew! sorry for writing a book, but I was on a roll! Hope this answers your question!