I have also run into this problem. Not only does it appear when clicking the name of the wiki at the top of page, but when you try to search for a page.
Searching for a page named duh, will return a url like this:
http://lostmywhiteflag.com/wiki/doku.php/?do=search&id=duh
And then you get the page that says "No input file specified". Clearly its that extra slash that is being appended after the doku.php, because removing that slash will then give me a correct page.
My config is pretty basic, as I'm just starting out my wiki. I don't have a base url defined, nor a base directory. Everything else works fine, and I can create pages by creating their links first. So really its something internal that is appending that slash.