PHPList comes with FCKeditor as the gui default editor. However, by default it is setup so that the spellcheck is only available to IE users. To enable for other browsers such as Firefox, follow the below directions:
Replace all instances of:
FCKConfig.SpellChecker = 'ieSpell' ;
Edit admin/.htaccess and add "spellchecker.php" to the list of files to allow access to.
FCKConfig.SpellChecker = 'SpellerPages' ;
If this is a linux box, then make sure aspell is installed. Edit "admin/FCKeditor/editor/dialog/fck_spellerpages/spellerpages/server-scripts/spellchecker.php" and update the aspell program path:
$aspell_prog = '/usr/bin/aspell';
That should do it.