The first, obvious step is accountability. For starters, a real name. At some point, we are going to need more: a domain, and address, and a footprint on the Web so we can see clearly who the police are and what they are doing.
Accountability is important, but Bernstein's list of mechanisms needs to be reconsidered. The thing you really need for accountability is a good, unforgeable record of what an account holder has done in the past. I bet Wikipedia already has this. Probably, every edit already is logged along with who performed it. If so, then Wikipedia already has accountability, and "anonymous" is a misnomer. What could be less anonymous than logging every single activity along with the name of who did it?
Looking for "real" names is a dangerous distraction. The other information in Mark's list is personal and frequently not helpful. There are exceptions; for example, you might use your real name to establish expertise in an area. There are even larger grounds for prejudice, though. Imagine you find out the human behind a Wikipedia account and you learn that they are, say,.... a religious fundamentalist? ....twelve years old? ....a political activist?
Additionally, keep in mind that some people live in uncomfortable situations. Not everyone gets to sit in a university and pompously declare to the world whatever is on their mind today. Some people need to profess the local faiths, and for them a pseudonym is the only way they can speak freely. If real names become mandatory, then many good contributors will simply be unable to contribute.
Overall, pseudonyms are not only acceptable on Wikipedia, but productive. I would go further and say they are a general feature of online life. If that sounds strange at first, then please consider a more familiar concept: separating private life from business. Is it really so much of a stretch to separate even more lives?