Increasingly important, but maybe add the option to choose which response codes are used, maybe include 403 also?

Use the official Internet Archive extension instead:
https://cup.aihedy.com/en-US/firefox/addon/wayback-machine_new/

When I click the browser back-arrow to go back a page in my browser history, the extension activates even though the page exists.

It hasn't been updated in a very long time and has probably fallen behind the way something works now, or else it has simply been broken for a long time.

It may work some of the time, but if it's not reliable it's not worth having. I tested it on http://www.fpsol.com/gems/webgems.html, which yields a 404 error. Result: nothing. On the other hand, the Resurrect Pages extension worked beautifully (and gave me my choice of Internet Archive versions).

It does exactly what it say!!

It'd be a lot more useful if it worked on connection failures (as such no HTTP errors).

It also doesn't work when the webserver redirects to some other page (an in-wesite error page or something else) without throwing a http error. Limiting it's use even more.

Even worse it doesn't seem to work on all 404 errored pages that I tried:
http://mkw.mortalkombatonline.com/games/mkt/

Works great

Works great on Firefox 51.0.1 64-bit.