Hello there!
I'm enjoying the game A LOT and right now I'm sticking strictly to vanilla until 0.4 versions of plugins are released (no plugins, callouts or mods installed). I know you must be overwhelmed with bug reports and support requests, but I'll leave mine here and hopefully will help you knowing that there are no external components involved, it's strictly vanilla.
I've seen a couple of posts of people with issues with controller buttons overlapping, but all of them regarding plugins like ELS. However this are the conflicts and bugs I've found in vanilla 0.4:
Can't cancel a blipped vehicle or blip another one. If you blip an incorrect vehicle there's no way to cancel it or blip the correct one, the A button does nothing. The only way to fix this is getting some distance so the car is unselected and then you can select another one. You should be able to blip another vehicle when one is already blipped, using the same button A.
Pursuit menu can't be navigated. You can open the menu with D-pad down, but if you press D-pad down again to move to the next option it closes the menu instead. Menu should be closed with B, not D-pad down. Right now you can only change agencies with controller, other options like tactics or lethal force are inaccessible.
Interaction menu can't be closed with B button. You can navigate back with B (for example from "Police radio" or "Vehicle" submenus to the main menu), but if you press B while in the main menu it makes the character punch instead. The only way to close the menu is holding Back button. I've sucker punched a lot of suspects and civilians trying to close the menu.
Edit: I was somewhat wrong. Menu navigation works, you can go back to a previous menu or close the interaction menu, but the character punches so it's still a bug.
Vanilla radio button (D-pad left) works sometimes. When you are in a callout D-pad left button works the same way as in vanilla GTAV, you can cycle through radio stations or hold it to choose one. But when you're not in a callout the button doesn't work, and the only way to switch stations is going to Interaction menu -> Vehicle -> Radio. Furthermore, when accepting a callout with D-pad left it also cycles to the next radio station. It seems like you disabled the vanilla GTAV feature (which makes sense, this way you have another bindable button and the player can still change stations through the interaction menu), but you forgot to disable it when in a callout.
Can't autocomplete plate numbers on the computer. Maybe I'm wrong, but I thought you should be able to autocomplete plate numbers with LB after performing a traffic stop the same way you can autocomplete person names after you ask them for an ID. Right now only person names are autocompleted. As I said, I'm not sure if it's a bug or it's intended, but it would be nice if you could autocomplete plates too.
That's all the issues I've found playing a couple of hours with an XBOX controller. As I said before, no plugins, mods or callouts installed.
Cheers!
Edit:
Goes without saying that I haven't changed the default bindings. I've took a look at them but I don't see how to fix the bugs, since most of them are related with menu navigation and those can't be modified.
