Brush Order
All brushes in UnrealEd have an order. The editor, when rebuilding the level, starts with the first brush in line and goes through every brush in sucession. The default brush order is simply the order in which you added or subtracted the brushes. To change the order of a brush, do Brush Context Menu → Order → First or Last.
Brush order is very important when you add brushes into a room. If you add the brush first, and then subtract the room, the brush you added will effectively be "erased" by the subtractive brush. If this happens, either set the order of the subtractive brush to first to make it subtract before you add the other brush, or set the order of the additive brush to last so that the room is first subtracted and then the additive brush is added in.
This case is rather simple, there are often much more complicated situations that arise. Just remember to try to follow a logical order when you build the level. If you plan the order well to begin with, you will never have to re-order your brushes later.
Note: there are exceptions to this. Sometimes brush order can be blamed for such things as movers which become invisible, and other such miscellaneous problems with geometry. To fix some of these, there is a good technique to try once you have finished building onto your map. First, simultaneously select all the semisolid brushes in the level and order them to last. Then do this again with all nonsolids, and finally with all movers. Rebuild afterwards. In this way, you'll have the brushes ordered in such a way as to never create conflicts, and there is a good chance that any display problems you originally had with brushes will be fixed.
See also CSG.
Flashman: Another use that I have found brush order to be a lifesaver/important is when you get halfway through building a level and then find that it would be really neat if you could put a window across a courtyard, but it means that your buildings need an exterior. Rather then try to do it all with subtracts, you can do one big cube subtract first and then build the outside of your buildings with adds/semisolids. Select all the new geometry and Brush Context Menu → Order → First.
N.B. before you build, make sure that no subtracts co-incide with any semisolids you have placed, if this is the case then select the offending semisolid and Brush Context Menu → Solidity → Solid
JustaAverageKid: Phwoo! This tool saved my life when I killed off one of my prime subtraction boxes (which held a bunch of other added material) by accident