I am also having this problem of erroneous broken links. What's strange is that a couple months ago I was cleaning them up after a major theme change and got them down from around 400 broken links to just a couple hundred. Then I got them down to just 17. Over the next few days, the number of shown broken links moved up and I am now at 144 and it wants to stay there.
Out of the first 20, only 3 are actually broken. The rest go right to the link when you click on the shown URL. I've tried editing the URL but that doesn't seem to do anything long term, although it will seemingly fix it occasionally and my count will go down for a few hours or days.
Anyone know what's going on here?