How to remove Firefox's "inspect element" button?

Solution 1:

Revisited in Oct. 2019: Both add-ons seem to be gone now, using devtools.inspector.enabled setting in about:config would be the best way to do this.

Revisited in Nov. 26 2014: Menu Editor seems to be deprecated. Menu Wizard looks like a good alternative.

Yes!

1. Install the Menu Editor addon
2. Open the options of Menu editor, make sure you are editing the Main context menu and then hide the inspect element entry

3. Drag the Firebug inspect option up to where you would like it
4. ???
5. Profit!

Solution 2:

This is not needed. As referenced: How do you disable the INSPECT ELEMENT option in the menu from Chrome and Firefox etc?

Type in about:config in your address bar and find devtools.inspector.enabled and set it to false

Solution 3:

Starting in Firebug 1.10, there is a Firebug setting that blocks the native Inspect Element menu item:

extensions.firebug.hideDefaultInspector

So, if you want it blocked, go to about:config in your address bar and toggle this to true.

If you want to see the native "Inspect Element" menu entry either disable/uninstall Firebug or toggle this to false in about:config.