The default configuration of the X server in Debian keeps a log of all the console output of the programs a user runs from their X session. It also keeps this log indefinitely. This is quite clearly a design mistake, because even ignoring badly behaved programs (those which are needlessly noisy are indisputably buggy), enough legitimate errors will eventually eat your disk. Plus the unjustifiable assumption that all programs out in the wild will be well-behaved, which is a nice hope but contrary to reality.
Sadly, this behaviour is also an ancient bug that has been, it would seem, forgotten about.
Anyway, here's a relatively simple method to fix that. As root, edit /etc/X11/Xsession. Just below the ERRFILE=$HOME/.xsession-errors line, add this:
if [ -f "$ERRFILE" ]; then
mv -f "$ERRFILE" "$ERRFILEOLD" 2> /dev/null
Each time the user logs in, the old .xsession-errors log file will be moved to .xsession-errors.old (overwriting anything already with that name), and a new one created. Thus it ensures that the file doesn't grow indefinitely, so long as the user logs out and back in at some point.