There are a lot of aspects to user interface design where Dwarf Fortress fails. It's still a great game. It just fails some basic usability testing.
Dividing them into rough areas, let me discuss some of the main problems.
Note: I'm going to be brutally rough here. Toady, please keep in mind that I love, love, love the game. I'm only being harsh because it's true, and because you need real feedback.
(1) Discoverability. How do new (or experienced) players find things they don't already know how to do?
(1)(a) The shortcut menu. It's impossible to find anything in the shortcut menu unless you already know where it is or what it does. It's possible to make the shortcut menu disappear and have no indication of how to get it back. The shortcut menu should be ordered in terms of priority, and commands that are more important than others (eg d)esignate) should be visually distinct.
(1)(b) The "long" help should be taken out behind the shed and put to sleep. It's useless. But then to make up for being useless, it's hard to navigate. Whenever I use it, I can't tell if it doesn't have the information I need, or if I just simply can't _get there_.
(2) Distinctions without differences.
(2)(a) Inspection. To look at a tile, you hit 'k'. To look at a dwarf, you hit 'v'. To use a workshop, you hit 'q', but to look inside it you need to hit 't'. I _still_ get these wrong during the game and quickly correct myself. I understand there are arguments for why one might want shortcut keys, but what i really want, most of the time, is a simple "query" tool that _does the right thing_ and, if it does the wrong thing, lets me quickly change modes. If this was a windowed program, this would be a great use for an inspector window that just showed everything under the cursor in one place.
(2)(b) Creating zones. Sometimes you create zones by setting anchors (eg mining and designation), and then other times you create zones by 'stretching' them via U/K/etc. Yuck.
(3) Specific areas of clumsiness
(3)(a) The jobs list. It was bad before, and now that it's getting bigger, it's getting worse. It turns out that often what I want is a trivial way to tell a dwarf "Hey, slave, if you don't have anything else to do, do the first job of any type that becomes available." Right now, that involves hitting the arrow key and return about 50 times. Conversely, sometimes my dwarfs will decide to not do the job they (and only they) are assigned to do, and there's no indication of _why_ they're not doing it. Without knowing why, I can't fix it.
(3)(b) Navigating through a 3d fortress. Building a fortress with a ton of z-levels is basically begging to be smacked in the face repeatedly. You either end up zooming around via <and>, or trying to psychically divine shortcuts ("Let's see, Ottar is cutting trees. He's _probably_ outside on top, then, although he might be on the way there and on some random level. I'll jump to Ottar and see if that takes me where I wanted to go. Oops, it didn't"). At a minimum, I'd love to have keys that meant "top z-level with digging" and "bottom z-level with digging." If it turns out these already exist, see section (1), "Discoverability."
That's my knee jerk reaction to the question "What's wrong with the UI?" If I come up with other things, I'll tack them on or edit this message.