Now that I have Firefox 49 or higher, how do I watch Netflix?

As wisely mentioned in comments: if you have this problem, contact Netflix support about it. It's a problem to be fixed on their side, and the more complains they'd get, the faster it get fixed.

A solution by GizmoChicken:

Is anyone able to play Netflix? With the original user agent it requests to install silverlight With chrome user agent it plays, but with tearing and high cpu load.

Netflix plays for me on Firefox 49 when using the following User-Agent entry:

Linux / Chrome 53: Mozilla/5.0 (X11; Ubuntu; Linux x86_64) AppleWebKit/535.11 (KHTML, like Gecko) Chrome/53.0.2785.34 Safari/537.36

Sometimes I have to hit "refresh" to start a video. I don't recall ever having to do that with Chrome. So it's still not perfect.

===================================== (edit by OP)

Before using the user agent string above (which worked) I had to do two other things.

1. Get Firefox to install the Widevine plugin by ticking the box on Preferences/Content labeled Play DRM Content.
2. Install User Agent Overrider extension. Then go to the extension's preferences and add the user agent string above.

Then just select the Linux / Chrome 53 user agent, go to Netflix.com, and Bob's yer uncle.

Edit 2: This also works on 32 bit Ubuntu! Woo hoo!

Edit 3: At least as of April 2017, 32 bit no longer works, but the user agent workaround is no longer required.

Edit 4: One of the many awesome enhancements in Firefox Quantum is that Netflix works again in 32 bit! (Dec 2017)

download vlc media player.

sudo apt-get update
sudo apt-get install vlc browser-plugin-vlc

I guess vlc downloads the necessary libraries, but Netflix now plays with absolutely no problem in Firefox 54.

Worth noting this also worked when I was running Firefox 47.