Make a file named "renamethis.sh". Its contents should be:
mv "$1" "$(echo $1 | sed 's/ \././')"
Set the executable bit:
chmod a+x renamethis.sh. Then, run something like:
find /path/to/dir -name '* .*' -type f -print0 | xargs -0L 1 /path/to/renamethis.sh
YMMV, no warranty express or implied, etc.
FWIW, the spaces are what makes this strange; as long as you don't have other oddball characters in the files names, you're good to go with this approach. If you do, you may want to consider something like a scandir/readdir loop in Perl or PHP, but the above script is the first thing that came to mind.