I'll start by saying that the tagging system on StackOverflow is generally very good, especially when compared with other sites. But at the same time there is some obvious room for improvement and I am very much in favor of making it easier for users to tag things correctly and harder for them to tag badly. For example, I think tags like
'and' should be banned, warnings shown if you use a tag with less than 10 other instances, tag synonyms checked at the time of a question is asked or edited rather than hourly, and a method created to propose tags for elimination or merging.
But does bad tagging really cost the site much? Obviously it costs the question asker, since bad tags can doom a question to oblivion, but that's not really what I'm getting at.
In the past I've thought that a lot of the site really depends on good tagging, but lately I'm not so sure. Google, for example, won't use the tags for indexing. And I've rarely used the tag search option on the site itself when I didn't have a pretty good idea exactly what I was looking for. This could be improved by allowing a tag wildcard search to match the interesting tags code. We lose some metrics data, but is that really important?
I think the biggest potential impact is when a question does not get answered because of how a new user tagged their question, and as a result we lose that user. Will this happen often enough to be worth fighting for?