Is there any way to search for unsolved tsumego on SL ?
There is unsolved problems, better is http://senseis.xmp.net/?info=Unsolved. These are pages with the unsolved template, but it never was on all unsolved problem pages.
If you notice the difference between the two links: There still is a problem that messed up all automatically generated lists with the data loss back then, churning the relevant pages and indexes lists them again. I did this for plenty of books, but could not be bothered for a list like unsolved problems.