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Firebug is the best add-on to debug your DOM structure, modify CSS on the fly...
If one is working with mobile and wants to change the user agent the add-on User Agent Switcher is great.
Want to view how your page looks in IE within FireFox here is an add-on to use IE NetRenderer
Want to check your pageweight and load time of pages you can use the following add-on Hammerhead. Alternatively one can use YSlow although personally I find it inconsistent.
For (X)Html validation here are some add-ons:
HTML Validator
Total Validator