In asking what I can do for the site, I thought I might make a grab for the Research Assistant badge. I'm a bit confused because it seems I've earned the privilege to approve tag wiki edits (1500 rep needed, according to my privileges sidebar), but when I edit the tag wiki I'm told that I don't have enough rep; my submission needs to be reviewed. Also, I don't see a Tag Wiki section of my review tab, nor is my own tag wiki edit appearing my my Review/Suggested Edits tab. Should I be able to edit a tag wiki without approval? If not, should the 1500 beta rep for approving tag wiki edits be changed?
To edit all tag wikis you need the Trusted User permission obtained with 4k reputation.
At 1500 you can approve tag wiki changes but that is part of the review process and at least a couple people need to approve the same change.
Prior to 4K I believe you can edit the tag wikis of tags which you have significantly participated in but I cannot find a reference to that right now. Searching.
Edit - search over, the answer is right on this very page.
Requirements for editing tag wikis are a bit confusing, but basically, there is both a reputation requirement and a specific knowledge requirement. From this answer on meta StackOverflow:
You will see that 20k users (Trusted users) will be able to edit all tag wikis. Further than that, the ability to edit tag wikis is not connected to your reputation level. The requirement to edit specific a tag wiki is:
You have at least 100 upvotes in non-community wiki answers with that tag OR you are in the top 20 answerers in this tag You have at least 2000 reputation points
I believe trusted user requirements on beta sites are lower (status completed on that issue), but haven't found the numeric value yet.