One of my favorite Firefox extensions for web design is the HTML Validator extension. I've mentioned it about a year ago on my Firefox web design extensions page, but this post covers it in more detail.
The HTML Validator extension offers status bar messages about HTML errors and warnings on each page that you view:

One you view source (Ctrl-u), you will see that the view source window is now divided into three main sections:

The bottom left pane shows a list of HTML errors and warnings. Double clicking on the warnings will highlight that section of HTML in the top pane:

The bottom right pane shows messages about HTML errors and warnings, with suggestions on how to fix them. Also notice the two buttons on the bottom right:

Clicking on the button labeled "Clean up the page..." will show the following window which shows the cleaned up HTML, the orginal HTML, as well as browser views of each. There are many options that you can set to control how HTML Tidy will clean up the HTML.

I highly recommend this Firefox extension for Web designers. You can download it here.
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Comments
I just finished one
I just finished one extension for Firefox which could perfectly cooperate with HTML Validator. It crawls through web domain and can validate whole domain at once togather with broken links checking and gathering other informations about processed web sites. By now it is only in sandbox, so it woud be very helpfull, if you could test and write some reviews on it.
It is available to download here: Web Doc processor
Thanks very much, I hope you will enjoy it.