I have had to solve this problem twice now, and I know I’ll forget again unless I write it down. So this is just to save myself future frustration.
Sometimes WordPress (or maybe it’s just my theme) sticks in a “continue reading” link even though I didn’t put it there (that is, in posts where I don’t deliberately add a More tag). The link doesn’t appear in the post when I go to edit it out, and I can’t find a setting to stop WordPress from putting it there automatically.
However, it seems to only do it when the post is untitled, or has the same title as another post.
Solution: give each post a unique title. Unwanted and useless “continue reading” link goes away.