Neither Stack Overflow nor CSTheory constitute an expert community on the topic of compiler design. On the other hand, Stack Overflow does constitute an expert community on many of the others--regex, android development, iphone development, etc.
Some questions applicable to compiler design do belong in cstheory (help! having difficulty with progress/preservation proof for language feature X), and some questions do belong in SO (help! having trouble with ANTLR). By and large, neither of these sites has become or seems poised to become a venue for serious compiler design discussion.
Why StackOverflow isn't an appropriate venue
StackOverflow is a boring place for people interested in compiler design. These people put in their 10,000 hours of coding a long, long time ago, and became bored of helping people out with the basics years ago. They're not trying to learn API or figure out why their program is crashing. People like this are not going to congregate in a venue wherein every third question is "debug my NullReferenceException for me, please".
Furthermore, searching for a few key compiler-design phrases (like "inline cache" and "baker's treadmill") on StackOverflow turned up nothing--StackOverflow is not already functioning as a compiler design community and has failed to build a meaningful compiler design knowledge base. If StackOverflow were going to meet this need, it would have done it already. It clearly hasn't.
StackOverflow is about short-lived questions--questions come and are answered very quickly. This is a poor model for design discussions on complex topics.
Why CSTheory isn't an appropriate venue
If you've designed compilers and spent much time over at CSTheory, it will be clear to you that questions about inline caching and garbage collector design do not belong next to questions about bounds 3SAT and hamiltonian tours. CSTheory is a discrete math forum, and its proponents would be happier if it stayed that way.
But a discussion about approaches to real-time garbage collection? An in-depth discussion of stack vs. register architecture for your virtual machine? StackOverflow tends to shy away from vague questions like this, and CSTheory would just close them as irrelevant, as they do any question that even has a hint of concern for implementation.
Compiler Design is, in principle, a lot like CSTheory
CSTheory is, unlike StackOverflow, a community of experts participating for the benefit of other experts and the field as a whole. In contrast, StackOverflow has some experts (the most prolific of whom are authors/educators first and implementors second), a ton of middle-of the road people, and a huger ton of flat-out newbies, and it's about answering questions that come up while writing code quickly in return for reputation.
CSTheory has a high barrier for entry--anyone without serious theoretical CS/discrete math background is going to find most of the discussion to be over their head. This is a good thing for them. The community that exists around this topic requires that condition to operate efficiently, and they've built it for themselves.
The compiler design stackexchange should be similar in character to CSTheory--a community of experts familiar with the latest in the theory and practice of compiler design addressing the gray areas and discussing the latest research together. Like CSTheory, compiler design should be a place for long-lived questions with many contributors and less emphasis on reputation farming.
Please don't kill the Compiler Design StackExchange--the compiler design community sorely needs a place like this to congregate and have high-quality discussions without being subjected to the SnR of SO or the strict "no implementation questions" attitude of CSTheory. Much like CSTheory, in order to attract the experts of the field, a more exclusive venue must be created.