If firefox does not correctly assume that your files are UTF-8 encoded, a possible solution (besides using a Byte Order Marker in your file, which is annoying for several reasons) is the following:
go to about:config and set the intl.charset.fallback.utf8_for_file variable to true. That worked for me.

This is related to the following bug report:
https://bugzilla.mozilla.org/show_bug.cgi?id=1071816

Note that the author notes that the extension only works "if the content is plain text". That means your browser needs to be rendering the file in a tab already, just without rendering the markdown elements. If it's downloading it instead, the suggestion from 7cac17 below, to add a MIME type for markdown files, worked for me (I'm also on Ubuntu).

Markdown that is super effective. Don't know why it is receiving negative reviews.

Nice add-on, woks fine for me. Maybe just missing the rendering of [TOC] tag.

For people who found FF keeps asking "what app should be used to open the markdown file", just check the solution (at least for Ubuntu) here: https://github.com/KeithLRobertson/markdown-viewer/issues/2#issuecomment-321940542

Utf8 - encoded Chinese documents display messy code, while GB - encoded Chinese documents display normal. Please fix it. Thank you for sharing this practical extension.
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The problem has been solved. An option to change the default encoding to UTF-8 in about:config: set the value of intl.charset.fallback.utf8_for_file to true. It is perfect now.

This add-on just works, I can now view markdown files with no additional software.

Works well. I noticed that "##Some header here" doesn't convert to an , but "## Some header here" does (note the space after the ##). But, at least according to daringfireball, that space *is* required, so...

Github markup renders very well. I'd like to thank the author, it works perfectly for me!

I was perfectly satisfied with the older "markdown-viewer" add-on until I found
out it prevented FF's multi-process (aka e10s, electrolysis) feature.

Glad I found "markdown-viewer-webext"! It renders perfectly acceptable, but different, HTML.