The first problem one seems to run into is getUserMedia() prompts, filed https://github.com/w3c/web-platform-tests/issues/5563 for that. Are there other things that we already know will be a problem and needs infrastructure work?

I think Chrome is pretty good on flags for that. The three most important ones are:
--use-fake-ui-for-media-stream (skips permission prompt)
--use-fake-device-for-media-stream (hello mrs pacman)
--mute-audio (mutes audio, no more beeps when running tests locally)

https://testing.googleblog.com/2014/09/chrome-firefox-webrtc-interop-test-pt-2.html and part 1 describe the basic setup.

The only thing missing on my wishlist is a way to control whether a fake audio/video device is present.

Is there any way to cause the permissions prompts to be denied?

my webdriver wrapper has it all:
https://github.com/fippo/testbed/blob/master/webdriver.js#L68

Fiddles with the chrome profile in bad ways :-)

#3, to cause permissions to be denied one can use 
  --use-fake-ui-for-media-stream=deny

That is still only a workaround. You do not replicate the way a real user would use the code. The final answer would be to be able to interact with security prompt directly with webdriver. That require an extension of the spec that is currently being done.

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