I can't reproduce this on other network sites, but it could be reputation related.
Normally "Edit Tags" doesn't appear, but when you hover your cursor next to the tags, it appears. Shouldn't this link always be here? Trying to scan your cursor for link is dumb. It also appears when you hover over the tags (which might be the original intent), however it creates an unnecessary "gesture" as you move your mouse over to the link.
*Red lines added for effect, doesn't actually burst into existence.