The spelling of the initial tags is...uneven. I don't have enough reputation to correct these tags but, it being a new site does anyone have the reputation to make the necessary corrections?
You can always make suggested edits to improve posts.
The changes won't take effect immediately, though - they have to be reviewed first. While you're right that we don't have users with enough reputation (500 in private beta) to review the suggested edits yet, you don't need to worry about that - there will still be community managers (employees of Stack Exchange) watching the site. They have moderator powers, so they will be able to approve suggested edits, and will do so until we have enough users capable of doing it that they are no longer necessary.
Note also that suggested edits can always be approved (or rejected) by the person who made the post.
So if you see a tag that is misspelled or any other problem in a post, go ahead and fix it (and any other problems you see with the post, of course). It'll get approved sooner or later, i.e. either when the OP sees the suggestion or when a community manager stops by.
So, to answer your title question,
Who corrects the spelling on the tags?
I do! And so do you!