The space you see is potentially not a normal space, but a tab, a non-breakable space, or one of some other similar special-purpose characters (no-orphan-space?)
To see them, try switching visibility on for all characters (the button looks like an inverted P).
You can copy one of those 'funny' blanks (shift & cursor, ctrl+C) and, using find/replace, paste it into source (ctrl+V), and put a normal blank into the target; that should clean them up all at once.