dot 3 and dot 4 fluids can be mixed.
Simply put, dot4 starts off as dot3, then borate esters are added.

Generally speaking, you can mix any dot 3 with any dot 4. However, there is some concern about different brands mixing together. Some of this might be due to marketing, some of it might actually be based in truth. Personally, I try to use the same stuff all of the time. When I change fluids, Typically there is a substantial color difference, and I continue to flush the system until what is coming out is the same as what is going in. I figure that vast majority gets changed then, and anything that is left is negligible.
Worst case, you're looking at lower boiling temps then you thought, and shorter fluid life. But since brake fluid should be changed regularly anyway, this isn't a huge issue.

dot 5 is the fluid that cannot be mixed as it is an entirely different chemical compound.