First I want to report something that I can only assume is a bug. I've only experienced this with one website but I'm sure it can't just be for this one. Reddit - usually when visiting Reddit for the first time on a mobile browser you are taken to the mobile page. There you can choose to visit the desktop page instead and a cookie is stored so that every time you visit Reddit from that moment on, you will always be taken to the desktop site. With Pale Moon this works until you exit your browser, when you start up again and visit Reddit you are taken to the mobile page once again. It's not a huge train smash but it is mildly annoying and Pale Moon seems to be the only browser that does this. I have no add-ons installed that do anything to cookies.
Facebook has a hard time with opening tabs in the background. About 70% of the time, opening something in the background will simply result in a blank page until you reload it, sometimes you have to reload two or three times before it actually loads correctly.
I also want to ask what kind of support for video formats as well as fonts Pale Moon has. Not a video format but gifs don't seem to play at all. I have also come across web pages that either display 'no mime type for this video found' or the video simply refuses to play altogether. May I suggest that you include an option to 'open with...' so that unsupported videos can be opened in an external player such as VLC? I have also noticed that certain fonts don't display correctly, usually emoticons but also various symbols. Sometimes it just displays a block or simply omits it altogether, making certain sentences tricky to decipher.
Now a couple of suggestions, these are little things that have annoyed me with every single iteration of Firefox for Android that I've tried. Please can menu items added by add-ons go into the 'tools' menu by default rather than cluttering up the main menu. Once again it's not a massive problem, just an annoyance. Maybe there can even be an 'add-ons' sub menu instead? Also, this is my biggest annoyance, a bookmark manager. I find it completely ludicrous that the only form of bookmark 'management' that can be done on your mobile is either adding or deleting them. In order to do anything else, you are forced to use your desktop browser. I know that you are working with the framework that has been provided by Fennec and a lot of things probably aren't possible or easily done but honestly these are my only two complaints about this awesome web browser. About the issue with certain app stores like F-Droid or Blackberry, have you considered creating a thread for this on XDA? XDA has an app called 'XDA labs' that allows devs to include their software for easy user installing and updating and as far as i understand they dictate zero terms to the devs and take nothing for it, it is simply a distribution platform. There is also a store called Aptoide, i see that someone has already put Pale Moon on it but it would be good to see an official channel for it. Aptoide is completely decentralized (hence the fact that you can find anything in it) so i doubt they there would be any dodgy terms and conditions involved there either. Also, considering that you are the dev and I am just a pleb user, feel free to disregard this entire paragraph.
I just want to end this off by saying that this is the best browser available for Android by a long, long shot and none of these bugs/format support issues/annoyances would change my mind and make me use something else. Best browser for Android and best browser for desktop too and I thank you for that. I have come across a couple of other bugs that don't come to mind at the moment but when I encounter them again I will report them, not to complain but to try to help to make this excellent software even better. Thank you.