This is not an issue with the spell-checker - this is an issue with your browser settings. In Firefox, go to Setting > General. Under the 'Language' section, make sure to tick 'Check your spelling as you type'. Once that is enabled, you should start seeing in-line form mis-spelling highlighted with red underline.

--UPDATE-- This one is very strange! It works on the freecycle.org form field called 'Post Title' but does not for the field 'Description'. My multi-line check is set to level 2. [about:config >> layout.spellcheckDefault >> set to 2]. I'm going to hazard a guess...this might be the way the form is setup there. I've never seen that before TBH.