What are current open problems in compiler theory?
In my experience, I've seen the following new compiler developments:


Work on automating data parallelism (or at least, reducing the amount of explicit work done by the programmer). This typically requires extensions to the language as well.
Work on extreme optimization strategies such as supercompilation or partial evaluation (where a program is collapsed via evaluation until it is reduced to its "smallest" form and then compiled)


I've seen a variety of work on things such as type checkers and so on, but I assume you're talking more about compiler-specific stuff.