This Firefox add-on enables you to spell check your Tweets! Works much better than your built in spell-checker.
To check spelling with SpellBound, choose the “Spell Check with SpellBound” option in the right-click menu when you are in a text field. You can also add the “Spell” button to your toolbar with the Firefox customize toolbar window and use it that way. Lastly, you can use the keyboard shortcut that is set to “Ctrl+Shift+F7″ by default.
This addon will set in-line spell checking for single line fields as the default behavior.