You do not need to install an extesnion, see

"Set-up of built-in Firefox spelling checker, if not working"

http://dmcritchie.mvps.org/firefox/tab_capacity/001_with_underscore.htm#spellcheck_jumpstart

after following the directions you will be able to check and fix the spelling in both multiline text areas and singline text areas as well.

With a bookmarklet, you will also be able to check the spelling (only) on web pages, or to add new words from a web page if you are sure they were spelled correctly on the web page.

Do you have a dictionary installed and selected?

• You can see which dictionary is selected if you right-click in a text area and open the Languages submenu.
• Open the "Add Dictionaries" link to install a dictionary if you do not have one.
• Make sure that [X] "Check Spelling" in the right-click context menu is check-marked.

You can enable or disable spell checking globally:

• Tools > Options > Advanced : General: Browsing: "Check my spelling as I type"

You can look here for dictionaries:

• https://addons.mozilla.org/firefox/language-tools/

See also:

• http://kb.mozillazine.org/Spell_checking
• http://kb.mozillazine.org/Dictionaries

Also see:

• Using the spell checker
• Spell checking (Mozillazine)
• Add a Dictionary: https://addons.mozilla.org/en-US/firefox/language-tools/

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Not related to your question, but...

You need to update some plug-ins:

• Plug-in check: https://www-trunk.stage.mozilla.com/en-US/plugincheck/
• Adobe PDF Plug-In For Firefox and Netscape: Installing/Updating Adobe Reader in Firefox
• Shockwave Flash (Adobe Flash or Flash): Updating Flash in Firefox
• Next Generation Java Plug-in for Mozilla browsers: Installing or Updating Java in Firefox