See summary. No idea why at this point. Perhaps it doesn't support .ico files?
Might want to have a look at high resolution icons at the same time.
This only happens on tablets as Firefox on phones doesn't show multiple tabs and hence no icons on them.
Also see bug 4583 which is probably affected by this.
This bug causes the icon used for "add-to-homescreen"-shortcuts on Android to be a orange square with a white star.
Firefox on iOS seems to behave the same way as Firefox on Android phones (i.e. not tablets). Add-to-homescreen does not seem possible with Firefox on iOS.
This bug only applies when using unsigned certificates. Both favicons on tabs and icons for add-to-homescreen work fine when using a proper cert. I updated the title to reflect this.
Moving from "Next" to "---" for discussion.
This is a general Firefox issue and not specific to ThinLinc. And since it doesn't happen with "proper" certificates we'll close this as WONTFIX.