This solved only part of the problem. I still get a lot of false 'nil'
from "(verify-visited-file-modtime (current-buffer))" because stat
returns ENOENT. One may argue this comes from my network, but the
problem appears only inside Emacs. I wrote a small program to call stat
a (huge) number of times on a regular basis (on a file previously opened
by the program), but I did not get a single error. Maybe the way Emacs
opens the files has something to do with that? I would be grateful to
you if you could suggest a few tests to find out why Emacs may
experience problems with stat while other programs do not seem to face
the issue at all (no EINTR, no ENOENT).

Note that, on this network, the problem is met by all Emacs users I
know, whatever their Emacs configuration. The computers are running
Linux 2.6.32-31-generic x86_64, under Ubuntu 10.10. The involved Emacs
versions are 23.1.1 (Ubuntu package) and 24 (git commit
78cda4761357774eb9daa19546a078f24aa1ee66 from 19 March 2011). I was told
the problem does not appear in Emacs 22, but I did not check it myself.

Thank you for the great work.

Best regards,
VM.