UPDATE: OCT-2019 to cover Firefox Quantum:
Enter about:config in Firefox address-bar and search for the keyword "full-screen". Identify following listing and change their respective values as mentioned against them below:
full-screen-api.transition-duration.enter - 0 0
full-screen-api.transition-duration.leave - 0 0
full-screen-api.transition.timeout - 0
full-screen-api.warning.delay - 0
full-screen-api.warning.timeout - 0
(Archival Notes) FireFox 42
Option "full-screen-api.approval-required", no longer hides the Website is Now Full Screen warning. In previous versions setting it to "false" could resolve the problem. They are putting a new option in i.e. (full-screen-api.warning.timeout "0") that will do the same thing, but it will be rolled out in FireFox 43.
You can change the fade in/out animation when going full-screen by setting:
full-screen-api.transition-duration.enter 0 0
full-screen-api.transition-duration.leave 0 0
Note/Warning - Defaults are 200 200 and 0 0 will remove them completely.
Keep in mind these are put in because they are a security features to help stop Phishing Attacks. So either wait till Firefox should enable "full-screen-api.warning.timeout" option in next few releases OR use above at your own risk...
1For Firefox version 43 onward the options are changed (refer to my comment below) – Amit Verma – 2015-12-16T19:04:35.413