1) Context-sensitive 'view battle' option. Right now I keep having to turn 'view fleet battles only if both sides are fleets' on and off, because for taking on precursor ships or fortified starbases I want to watch and see how my ships are actually stacking up. But when I'm taking out freighters, transports, that sort of thing it's a total waste of time. What I'd like to see is a 'View Battles if Close' option, that would have you watch fights where both sides(or just yours) are liable to lose ships.
2) Disable the end-turn function when certain full-screen windows are open, I've accidently ended turn while viewing a planet or building a ship (by hitting enter) several times and it's a pain in the butt. Also, I've had a lot of inadvertent end-turns after clicking 'Done' on certain screens and popups and then accidently double-clicking while my mouse was hovering on the End Turn button; maybe if it'd ignore clicks for a split-second after closing those windows, that'd prevent that.
In times of war this can be a major issue, I literally lost a planet whereas if I'd been able to play out the turn as I was planning to I would've intercepted the lone un-escorted transporter with ease.
3) Maybe some sort of diplomatic 'balancing' when it comes to Influence Base Rushing. The AI will do it even if they wouldn't dare start a war with you, but even though it's a basically aggressive act for them to build those bases, if you blow up one you'll start a long and costly war. Either they need to forgive it easier and allow a peace treaty under some circumstances, or, you need to be able to threaten or cajole them into stopping the construction of them in your territory.
Also allow us to overwrite 'core' ship names, or add a number or something to the core ship names to free up names that we might want. I was pissed I couldn't choose to build a Destroyer, or a Missile Boat.

If the core ship design was called 'Destroyer (Core)' instead, then I would've been able to have my Destroyer, and Battleship, and Missile Boat, and other names that I honestly wanted to use in my last game playing the Terrans! (I was following a theme of their space navy harkening back to their ocean navy, so I wanted to use the 'basic' names for several designs)