Bill,
Maybe I can help Glenn out a bit here.
> I'm just curious as to when you've seen angled walls "mess up" the sound more than if the same room had had parallel walls. <
Having angled walls is never bad, but it may not help much either. The two rules of thumb are:
1. To avoid flutter echo between two parallel surfaces, each wall needs to angle about one inch for every ten linear inches. Less angle than that is never bad, but it won't fully stop the flutter echo.
2. The other reason for angling walls is to deflect first reflections from the side walls to behind the mix position rather than toward your ears. The same goes for the ceiling. To achieve this you need at least 30 to 35 degree angles. This article on the RealTraps site explains it in more detail:
www.realtraps.com/rfz.htm
The main reason to angle the walls for #2 above is to avoid first reflections and the comb filtering it causes, but without having to make the room more dead sounding as would happen with putting absorption at those reflection points. Another way to reduce the effects of early reflections is with diffusion instead of absorption, and that too avoids making the room more dead sounding. Personally, I prefer a control room to be on the dead side, but some people prefer more of a live sound. So angling or diffusion are two ways to achieve that.
--Ethan