# output "NOK" if standard error has any output; "OK" otherwise:
errlog=$(mktemp)
somecommand 1>> "$stdlog" 2> "$errlog"
if [[ -s "$errlog" ]]; then
# File exists and has a size greater than zero
echo "NOK"
else
echo "OK"
fi
# Done parsing standard error; tack it to the regular log
cat "$errlog" >> "$stdlog"
rm -f "$errlog"