Here's a list of things I've found to be slightly annoying.
#1: The "Rearrange HUD" feature - It's great and all, but when I'm rearranging my HUD, it shows big green boxes, it doesn't show what the UI/HUD actually looks like, and in some cases the box isn't the same exact size as the UI/HUD piece. Also, it'd be cool if there was a feature that created a "Save layout" file that I can then share with my other character(s).
#2: The Dilithium/ZEN Exchange - It's a wonderful addition to the game, and I love it, cause when I have left over zen I'm not using, I convert it into dilithium, for later or for projects, but when I want to sell dilithium for Zen, that takes time partly because it's not an exact "I'll give you 25D for 1Z", it's more of "I'll give you how ever much for D, for 1Z." And we're trading with other players, and so far the demand for Zen is higher than dilithium. I kind of wish the exchange was a little different, and was a little quicker.
#3: The Dilithium Store - The UI for the store, and some other stores are a pain to navigate, in order for me to go from say, request a ground phaser weapon, to say Ship consoles, I have to close the window, and start from the main UI of the store. I would love to see the store UIs take up a similar "Filter" system like the PvE screen has. Have all of the ground, space, and spec stores in one UI, but each tab has a filter that filters down by type and use. I also noticed there aren't many MK XII times in there, most of the time it's MK XI, and some cases MK X.
#4: Duty Officers - I love it, it really adds to the game for those of us who've maxed rank, but we can only do a max number of 20 Assignments, which is fun, but there's been times when I wish I could have an extra 30 assignments I can have my duty officers working on. I also wish there was more things I can earn from finishing assignments, like have some assignments that give Omega points, or lobi Crystals, maybe even ZEN, I'd enjoy being able to earn a small amount of zen in some missions.