I've finally been able to play for more than 15mins or so without a crash, and so I can finally give some feedback. Before I start, I want to say that I have the utmost respect for Stardock and the work they do, and I'm certain this will be an amazing game. I will be very honest in this post, and no offense is intended.
1. Information Transparency
This, in my opinion, is by far the most critical area that needs improvement. There has been some progress, but I frequently feel that I am missing key information, or that this information is too difficult to find. If players don't understand what's happening and why it's happening, it is very difficult to give useful feedback on the beta. As one example, I frequently find I'm spending a fortune on "city upkeep" and I have no idea how this is determined or how to minimize it. Also, I don't know what resources help with building which things, and this can be very frustrating.
2. City Building
In a recent game, my starting location was next to both an orchard and fertile land. I was hoping to build a huge city here, but to my dismay I required more houses that I had tiles for and city growth stopped. Also, the city had virtually no specialization, it was just highly populated, but apparently not populated enough to build a house on a new tile. This is very frustrating! One quick fix may be to make housing not count towards usable tiles, and limit city growth by food production (food makes the most sense as the limiting factor anyway). Also, city-spamming seems to be well under control with upkeep costs and food requirements, but the penalties seem a bit too harsh on outposts that are only meant to acquire resources. I would also prefer that usable tiles are set by population and the "city level" determines which buildings can be built. This would allow the highest level cities to continue to grow if they can acquire the food. In the current system, it is just too difficult to build fun and interesting cities.
3. Resources
I don't know what the vast majority of the resources do, and that may be fine because it is still an early beta. However, there are some important resources in the beta and I really wish I understood them better. I often try to build a lumbermill as soon as possible to aid in building construction, but again it's not apparent how much this helps. Also, with the current city building implementation, resources collected with outposts seem to have more cost than benefit. Resources should be exciting and rewarding! It may be a neat idea to categorize resources so that stone, wood, clay, marble, etc all aid in the construction of buildings(and may eventually influence how they look). This could give many resources multiple uses and help make the resources you collect define your empire. Maybe unused resources could also generate income each turn, this could help offset the costs of building outposts.
4. Technology
In the current beta, I feel very disengaged from technology research. I like the concept of randomness in research, but the current system is a bit...weird. It is still fundamentally a technology tree, and the randomness only introduces delays rather than making a real difference. One possible change would be that you choose a tech to research, and it has green, yellow, and red techs that become possible(based on color) to research once you complete the current project. This way research is deterministic, but what becomes available next is random. This is similar to the "research web" idea and different techs could open different options. Also, the random inclusion could be determined by techs that are only opened by a few other techs, and if every attempt fails then that tech is lost.
5. Magic
I haven't had much time to try this out too much, but I generally feel that shards need a generic benefit + specialized benefit. Requiring them for casting spells is an idea I like, but I think they should also boost mana/research/spell points or something as well. If I have a fire book and discover only air shards, they shouldn't be completely useless to me. I'm still waiting to see how essence will come into play. Personally, I would like a "conservation of essence" system, where essence is acquired through quests, exploration, or stolen from others after defeating them in battle.
I don't really have any comments on dynasties or quests yet. I actually haven't received a single quest. I do like the concept of governors, sort of turning cities into fiefs for your vassals. This could really help make cities unique and interesting.
With that, I'll conclude my post. Again, no offense is meant, and I'm sorry if there is redundancy with other posts on the forums. I am really excited about the game and thankful that Stardock is so passionate about it and willing to have open discussions.