I think the biggest computer security problem today is not a technological problem. It's us (and the way we use the tools we already have). We have created some pretty fantastic solutions to protecting and obfuscating information from each other. (Language being the oldest one I'm currently aware of.)
A good example of my point: The recent problem with MtGox (a marketplace for trading cryptographically secure currency) tanking was a human problem. (FYI, a guy who had access to the MtGox databases allowed his personal equipment to become compromised with MtGox backups on it. These databases had a poorly designed security implementation.) Until we can create completely intuitive security (hard), create idiot proof technology which protects itself from the user (harder) or appropriately educate people on their actions at the time they are making them (overwhelmingly impossible to do well at scale); we will have problems which are arguably much more important than solving any other problem.
(This depends on your point of view and what your metrics are that describe something as a "problem".)
