I think it would be good to just have an option to replace/remove spaces in names during FTP transfer, then you don't have to change them on your local filesystem.
How does that sound?
That sounds like a good solution, although we actually use Transmit rather than PM to FTP the images...
Why?
A couple of reasons - some of our clients use sftp, and also Transmit seems more robust if transfers stall or need to be cancelled. The queue also gives visual feedback as to which server the images are going - useful when you have to send to 20 servers as we do every day.
We don't yet have secure FTP. The latest version should cancel much better since we added non-blocking socket communication.
What kind of visual feedback does Transmit give?
As for your original problem, eliminating spaces from filenames, I think if I were to add Find and Replace on filenames, you could find spaces and replace them with '_' which would solve your problem.
In the meantime, you could put the filename into an unused IPTC field by using the {filenamebase} variable in the IPTC Stationery Pad, and then you could Find and Replace a space with _ in only that previously unused field. Then you could batch rename using that IPTC field. Then if you want that field to be blank again you could apply the IPTC Stationery Pad again to clear out that IPTC field.
Example:
Unused field is "Edit Status:" Select all of the images you want to work on. Open up IPTC Stationery Pad. Set the check on the Edit Status field. In the Edit Status field put: {filenamebase}
Click on the Apply Stationery to Selected button. Close the IPTC Stationery Pad dialog.
Open up the Find and Replace panel (Edit->Find and Replace). In the Find: field enter a single space. In the Replace: field enter a single _ (underscore.) Set only the Edit Status checkbox. Do the Replace. Close the Find and Replace panel.
Rename the photos (File->Rename Photos...) entering {editstatus} in the renaming string text field. Click the Rename button.
If you want to clear out the Edit Status field, you can open up the IPTC Stationery Pad again, clear out the Edit Status field, and make sure that its checkbox is set. Then click on the Apply Stationery to Selected button.
It's a roundabout way of doing what could be done in one step with a Find and Replace with filenames but it will work fine.
HTH,
-Kirk