They're patching things in quickly so I'm willing to give them the benefit of the doubt, though May does seem really soon I admit.
Here's what I think has to be in at release:
1) Tech Tree: All of it. Pretty obvious many of the lines are closed, and many of the techs don't actually do what they say. Patch 5.3 will be a great step forward, however. The Prototype system needs to be fully implemented, and shown on the tech tree. Having a reason to fight for resources will be a HUGE improvement in gameplay.
2) Buildings: For starters all buildings must be double-checked to make sure they are actually doing whats in the description, and that it's clearly presented. Most of the work is on the modifiers being clearly presented, but some buildings(Iridium influence buildings for ex. have broken adjacency bonuses). Military buildings need much clearer description and presentation. A lot of buildings also need a good balancing pass. Some are real strong, and others are worthless.
3) Modifiers: All modifiers need to be clearly presented and working correctly. Planetary bonuses:(Manufacturing bonus bugged, and not presented), Influence is working but poorly presented, Tourism bonus not shown(working-maybe), Trade bonus(have to know where to look), Science, Approval, and Growth(Good job on these 3). Ideology modifiers may need better presentation as well.
4) The AI: On release players won't have the option to sit and watch the AI like we can now. But suffice it to say, it's a ways from there yet. Every patch is certainly making great strides though. You could also lump-in, squashing cheesy strats from being viable.
5) Win Conditions: Have to be fully implemented, and bug free. Diplomacy, UN, and Influence related victories have a lot of fleshing out and/or balancing left to do.
These 5 things are absolutely core.
Less important, but still pretty damn important:
1) Ship Designer/Ship List: All of it is a bit unwieldy, even for an experienced person. The ship design is buggy. Bug1: Parts auto-symmetry themselves, and the symmetry buttons are grayed out, so you can't change it. Ex. You attach 2 beam weapons, but the ship shows 4. The buttons to turn this off is grayed out, and doesn't work. Bug2: In edit ship mode, sometime it selects the first attached part at the bottom of the screen, and you can't select the other attachments at all. Have to start from scratch.
The list of ships to build needs better filtering.
2) Ideology: Fix all bugs and descriptions. Then have a good balance pass.
3) Racial Balance: Once the AI is mostly implemented(not there yet), these guys need to be tested A LOT. Nothing worse than knowing from the start, that it's really just those 1 or 2 races you have to worry about.
4) UI Presentation: I think they have most of this stuff ready, but we haven't seen it yet. The proper notifications and the like all need to be in there.
Much less important, but what makes a good game great:
1) Anything that affects a players sense of immersion. If you don't get lost for hours, thinking you're the true ruler of "Insert Faction Here", then I say hold off on official release. Some of the above comments may fit into this category. A few of them may even be petty, but if it breaks immersion then it kills the true experience for the player.