Unfortunately, you can’t! (update; you now can)
It’s a bug in Firefox and there is no work-around to fix this besides from fixing the source base itself (see below).
Also see Jonathan Watt’s blog (who is working on this):
Known issues:
- the default CSS styled appearance still needs work, and native theming (giving the slider the appearance of the operating system’s
theme) is still to come …
In a reply to a comment in his blog about this very same issue he states:
Right now you can’t – sorry. I’ve filed bug 932410 to make that
possible.
At the moment of writing there appear to be no progress on this and it’s not known when a official fix will be available.
Update
Since this answer was posted the bug has been fixed. You can now use (as stated in other answers, but I include it here for completeness):
input[type=range]::-moz-focus-outer {
border: 0;
}