The current way to register for a contest redirects a user (when not logged in) to login page when she/he clicks on the register link near the top right corner. However, this doesn't register the user nor redirects to the registration page. The problem that I find with this behavior is that it is inconsistent with the behavior had the user already been logged in.
I have missed a couple of contests due to this. I intended to participate in round #141 and only realized that I wasn't registered when I tried to submit a solution but couldn't find a "submit code" option. I think redirecting back to the registration page after logging in would help me not miss out registration for contests.