Okay, so I'm actually rather tired of trying to use Discord as a decent chat client. The UI is rather poorly designed for a chat app, and the thought that it was never meant for more than a voice chat system really shows in the desktop and web app UI.
For starters: The nicklist (user listing) and servlist (server listing) panes are completely static sizes, allowing them to completely overtake the chat area. No, I'm not exaggerating, you can completely obscure the chat area with a small enough viewport. You can't hide the nicklist or servlist, either.
For tablets where people need higher zoom levels—somewhat akin to lowering the resolution—this can make Discord completely unusable. The default should give the chat pane a minimum width (min-width), and auto-hide the nicklist and servlist if the viewport shrinks to a certain point. It's trivial to impliment this in CSS, or any programming language (C#, ObjC, C++, etc…)for that matter.
Then there's the whole "auto-load every old message in a very cluttered chat area" problem on loading a room. Yes, for a feature, having old messages is great, but apps that do this typically show some sort of clean break between old messages and new ones. Hell, they typically have much better spacing for the messages themselves.
There needs to be a clean break when you log in, and there needs to be more spacing between messages.
Now, don't get me wrong. Discord is a great service, and I'm all for seeing it grow. That's why I complain about these things. Unless I'm just utterly taking the piss out of something, I'm typically criticizing a product because I know it can be better. It's just like how I criticize Mozilla about some of the decisions that I think are bone-headed.
Personally, I'll still prefer IRC over Discord, but for a Skype replacement, it's one of the best options out there…outside of Mumble, which I endorse more simply because you can roll your own server. Most people won't use XMPP, even though you can do voice and video calls over it rather easily, so I don't try to push that too much.
And there ya go…