Hello everyone. I actually ignored Alpha stage because the game was so undeveloped, but in current state of beta that seems to be a way better game than GalCiv2 was.
Disclaimer: I clearly realize that not all things are easy/possible for the developers, and that some things have clearly been already stated and discussed; I just try to summarize what I found.
I guess I will make a small list of advantages and disadvantages in general before everything else.
So, the pros are:
1. Way better graphics. Especially the vids, now you want to see them and not ignore.
2. Sid Meier's style of colonies and shipyards management (well, addition of the shipyards themselves), removal of tax from empire government menu and that awful "industry occupancy rate" or whatever it was called, I don't remember (where you set the %, to which you use the capablities of labs and factories). As a result, a more interesting way of economy management via other methods.
3. Revision of resources management and the "relics" idea, making powerful bonuses harder to acquire.
Cons:
The game is too much like GalCiv2. I understand that it is basically the same game etc., but the following things are there, and they are hardly reviewable.
1. Ship Designer is beautiful, but makes no practical sense.
2. Trade. Just send the freighter and that's all? Trade licenses are just another name for the same, old, and boring trade routes?
So, the bugs, imperfections and incompletenesses:
1. No money is deducted from your account when you upgrade ships. That makes it very easy to cheat by designing the cheapest possible ship and make top-tier armadas in no time by freely upgrading them. I don't use this, but you really got to fix it guys.
2. Survey ships way of behaviour. Some anomalies are being ignored.
3. Era bar. I don't know whether this is a bug or no, but the actual fact that researching Disruptors (whatever the tech is named), which are basically rather early beam weapons, made me enter the Age of Ascension, makes no sense.
4. Allegiance and influence corellation and interconnection. I had a situation, after some galactic event, that like 10 planets joined me at once. It was a small map and virtually half of the galaxy.
5. Planet generation. Abundant means ABUNDANT. Not 1 planet per star, often non-colonizeable. Same applies to the amount and the location of stars. That's not the hardest thing to do, people, and you really gotta fix it as, possibly, a primary issue. 
6. No colony management screen! The governors/colony managers are yet to come, as I see, but we need that screen. That was the best way to get the job done in galciv2.
7. I still do not fully understand how exactly the resources are used, though, i guess they give some effect. However, it would be interesting to know how their amount is affecting what.
8. Ships inside the nebula. That has been reported many times and I don't think it is needed to elaborate more.
9. Lack of any predefined hotkeys or the possibility to assign your own.
10. Game crashes sometimes on larger maps.
11. There are issues with Government screen, the general adjustments are not always seen in the corresponding colony screen.
Suggestions and "want to have's":
1. As already said, the colony management screen, sortable through different columns.
2. The starbase management screen, since SB's play a significantly more important role in GalCiv3 than in previous versions. If possible, intergation with the colony management screen.
3. Reduce the black holes radius on small maps.
4. Approval/Tourism/Influence/Diplomatic Researches should be more interconnected and the scheme shall be more clear.
5. Fixes to Power screen. What do these numbers even mean? As far as I understood it, some part of the score is dedicated to military and some to economy. Could you make it more clear?
6. Better autopathing for ships. You dont need to go through the entire giant nebula when you can ignore it and get to the relevant place faster.
7. Make something with trade. Add corporative licenses, unique goods or things like them. This is the matter where no visible changes were made compared to GalCiv2.
That is probably all for now. The post will be updated and reviewed as it goes.
Thanks,
Hummer