The system is a decent one for classifying questions. The issue about finding things is that since questions are limited to 5 tags, you generally have to have a fine-grained search criteria to find things.
This means you can't really go "browsing" for database questions; instead, you can browse SQL Server questions or MySQL questions. Remember, though, that browsing isn't the point of the site -- the point is to be able to find an answer to your problem, and that normally means you already know the fine-grained details to use as search criteria. I.e., you don't ask "How do I fix the problem with my database?" (which would be closed as 'not a real question' within 30 seconds); you do ask "How do I fix the performance issue when I search on column z in my SQL Server database?" You can quickly pick out the major topics from your issue and filter the questions in the system accordingly.
With regards to keeping the tags orderly, yes, it would appear that the system is a complete mess, but actually it's not so bad all things considered. I think the mess appears bigger than it really is because the total quantity of information in the system is so large; but relatively speaking, it's not bad. SO is a repository of (currently) nearly 650,000 questions with over 80,000 users (>= 10 rep), so having only 71 open tag merge requests right now isn't out of line. I've done my best to clean things up, and with the help of everyone else, we've been slowly chipping away at the requests.
That being said, we can do better with a little automation and management. Two key features are currently planned: tag synonyms, which will eliminate the issue of singular/plural tags, as well as a whole host of other issues such as localized spellings and common acronyms; and a tag blacklist, which should prevent eliminated tags from showing up again and reduce the amount of noise in the system. IMO, we need both these systems for the tagging process to be really effective.
As far as searching for questions with given tags go, there are some powerful search tools available already (some of which aren't available using the search box). See here for how to use those search options.