Good list.  A UI improvement would really increase the enjoyment of the game.

I really agree with improving the shop interface.  Ideally there is one screen that handles all shopping, trading and equipping.

The other UI improvement I would like to see is a much more visible way to see the destination of units.  Ideally, a big red arrow would pop up between the unit and the destination.  Also, a toggle button (preferably a hot key) to turn on all arrows at once.

On the build menu for cities, sometimes it shows the build queue and other times is shows the city specs.  Ideally, they would both be up at once.  If one of the bottom two menus needs to be replaced, the one on the right would be better than the one on the left.

Two things I would like to see changed:

1) Whenever a player hovers over an icon of anything that requires resources (for a building or improvement), the UI should display the number of resources required and an icon/picture of that resource. What we have now is a number and a string: '25 materials' - this looks cumbersome and I always catch myself reading the word. The brain can identify pictures and symbols faster than words - it will be easier on the eyes this way.

2) Instead of having a huge message box pop up every time your sovereign finds goodies, there should simply be an animation of the icon of the resource they found plop into the sovereign and fade away.

I think the UI needs some more love (hear: tweaking) to cut down on the number of clicks to perform usual tasks. For the record, I'm a front-end developer myself, so I do realize it may be more complex than it seems, but at a glance, it seems there are a few reasonable ways to achieve that:

Break the infernal cycle shop<-->inventory<-->trading

• the shop window has plenty of space to embed an inventory window, allowing to (un)equip as needed.
• Allow switching hero in the inventory window
• The trading window would benefit from showing the full inventory as well; you could simply highlight what is equipped (heck, let us change it as well!). Additionally, displaying full heroes' stats there would mitigate another issue: I see currently no easy way to compare your heroes
• IMO, the absolute best thing to do would be to merge the inventory & trading window (trading window = 2 * (inventory window + hero switching) + drag&drop), and make it available in the shop (fire the shopkeeper if need be!)

Add some shortcuts

• when you double-left click on the city center, you get the building panel (lower left), while double-right click gives you the training panel. This is a fine idea, but it would be way more efficient if we had the same behavior on the city icon (upper left on the screen), and not just the current single-click focus and center.
• the same principle could apply to heroes icons (circles right above the lower menu bar) w/ double-left click to get the inventory and double-right click to get the spell casting window

Review some windows

• The building panel should be tabbed so that you can get to the training panel in one click (and vice-versa)
• I would also question the need for "intermediate" windows, like the city one (upgrade+train+rename): while the city is selected I would make the (tabbed) building panel visible at all times.

Hope it gets to the right peeps!

Cheers!