I think the main thing is that the game doesn't explain at all, from what I could see at least, that your bonuses are subtracted from the DC automatically. I was really confused when I first started playing when the DC was 5 and with my +5 bonus I still failed the roll. The way they have it now with the bonuses being subtracted is fine, as long as they add a tutorial or something that tells you that's what's happening. As for advantage/disadvantage I agree that both d20s should be shown on the roll screen. Seeing a 1 on the lower dice when you have advantage is nice.
As for showing DCs ahead of time, I think they should use the system from the book SwordSaintSilver said, and say how difficult the check is going to be in an abstract way. And then, your character can do an insight check for conversations or investigation for traps/locks/pickpocketing to get an exact DC. I would like to be able to see if a door/trap/chest is even within the realm of possibility to open instead of breaking all my lockpicks then reloading. Pickpocketing right now actually shows you the DC needed for each item you select, which makes it way too easy to just enter turn-based mode and completely clean out a merchant. Having to at least do an investigation check to get the DC would make it at least a little harder.
On a side note, stuff like friends, charm person, detect thoughts, and similar spells really need an option in dialogue to cast them. Currently, if you want to use Friends you have to know a conversation with a charisma check is coming up and cast it before talking to them, and if it's your first time playing how could you possibly know that, unless you're going to save before talking to every npc and reload if they have a check, which is insane. Not to mention if it's a conversation that triggers automatically when you get close there's a good chance the conversation will trigger before you're even within casting range of Friends, making it useless. In 5E, the Friends spell specifically says the person you cast it on knows you cast it on them when the spell wears off, which is the entire drawback of the cantrip. It makes you weigh the pros and cons of having advantage on the charisma check vs what that npc might do when they find out you charmed them, like are they going attack, get a guard, raise their prices, run away, etc.
Very interesting idea with the investigations, though might be seen as unwieldy to some, but id totally be down for a tiny button next to checks like that for a one time investigation check
As for the social spells, seen that sentiment before and totally agree, they'd be dumb to leave it as it is now, at the very least they need to make the ones that create dialogue options last longer (granted I'm just agreeing with the sentiment here, haven't actually played with any of those spells yet myself)