I'm just in doubt about the file: /usr/share/emacs/site-lisp/auctex/.nosearch
and I can't understand this issue right away.
This file is installed by the preview elisp library, and is intended to be in the subdirectory for its code. The main auctex code doesn't install such a file. It gets into this place because the two libraries are merged in the same package.
So, I don't understand whether /usr/share/emacs/site-lisp/auctex/.nosearch is an obstackle for the auctex library.
I'm writing this bug report down as a note to think over later.