I'm putting a few suggestions in one note because they are things I think can make it easier for a new player to learn the game mechanics. They are things which may not matter as much after someone is used to the interface.
Beta3 is my first time in Elemental. I didn't read the manual or keyboard notes, just jumped in.
Before making suggestions I want to say: Awesome! Much of the UI is intuitive and the graphics are wonderful. The extensive use of tooltips is great, making it easy to learn many things.
Learning to walk. This took a bit more thinking about than I feel it needs to. There are a few factors which combined to make this a tad awkward:
1) A unit can move within a tile or to a new tile. With no grid lines it can take a moment to realize what's happening. (Of course the target icon for new destination helps but the overall feel wasn't immediately obvious to me.) Suggestion in next point would alleviate this.
2) Movement is tile based but the default setup doesn't show grid lines. I found it much easier to walk comfortably once I turned grid lines on. I suggest that grid lines on be the default setting. Users can turn them off after they feel comfortable with walking mechanics.
3) A unit's remaining moves in current turn aren't clearly displayed. I'd like to have a prominently visible X/Y (moves left / unit range) displayed somewhere. (I did some clicking around on my first recruit wondering why the fool didn't move before realizing he was out of movement.)
4) The time it will take to reach a multi turn destination isn't clear. It would be nice to have it displayed on the destination.
5) Can't walk on mountains. This confused me because it is possible to set a mountain as my target for a multi-turn move (bug?) The unit simply stopped before climbing the mountain. A message saying something like "mountains can't be climbed" when trying to go onto one would make the rule immediately obvious.
Learning to improve a town. When I first clicked on an entry in the city improvement list I didn't realize what was happening. It wasn't obvious to me that I had to click on the "proposed" improvement on the city map to make the build happen. I suggest that after clicking on an entry in the city improvement list, the proposed improvement should be auto-selected and the cursor move to it.
The "C" (center) command. After playing a while I read up on command keys and discovered this. In subsequent play I found it very useful. I have two suggestions for it: a) Make it also work for cities. 
Make it easily discoverable by new players, perhaps by adding a second button beside "Done" on the Unit details and City details popups, labeled something like "Center On (C)".
