During an AI's turn, while as a player we can continue to look around, check out and edit planets as well as many other things, the UI does become laggy/unresponsive at times, the longer the game the worse it gets.
I would like to suggest that the game removes player control once you hit enter, black out the screen and place the turn counter in the middle of the screen during this process. (Similar to how ES and ES2 are during AI turns)

AI does not aggressively go after Relics, most of the time (Unless it falls within a mining bases radius) they will leave them be.

AI still prefer's 1 shipyard per system, not going the 5 planets per shipyard is better route. If at war and they lose all their shipyards, every planet they have will start producing a shipyard.
AI Silicon Races do not destroy Arable Land or Farms.

AI will consistently over produce/buy Freighter ships, in-excess of twice the amount it needs. (Seems this applies to Colony ships too, probably more to do with others beating them to planets and the AI not understanding it needs to re-purpose them)

^^ This also happens to unused Freighters. (I decided to leave them be, they eventually got moved between turns 92 and 104 over 50 turns of RP and population growth wasted for no reason)

Abilities a race may have are missing from the Diplomacy and Espionage report screens. (It displays Traits)

There is no tooltip (breakdown) for total mass on a ship, not on the mass bar in the designer or when you hover over hull size in the shipyard.

When going to a ship and selecting details, all but one of the tooltips are missing from the stats in the stat window.

Planet features are no longer colour coded. (Red been Military, blue Research etc)
Planet improvements are no longer colour coded. (Mostly the newer improvements)

Additions:

The in game music does not play all available "tracks" for an Era (Early, Mid, Late) the game seems to select 3 maybe 4 tracks from the available list and just repeats them until the next Era.

Players STILL get charged for an improvement an AI rushed on THEIR turn if that planet gets culture flipped during the AI's turns.

Treaties that expire are set to low priority in the notification system when they should be high priority. (This is why people keep moaning about open borders giving no warning when it expires, most of us have notifications set to mid - high only to reduce the clutter)

During trade negotiations the AI over evaluates the value of special and strategic resources, they always think x resource is worth x regardless of the price in the Galactic Market.

If you select a technology to research that is quite far down a tech line that the game then has to research more than 1 tech to reach your selected tech, when you either have Ideology points to spend or check out the Ideology trees the game will exit you to the technology screen not to the galaxy view if you have already researched 1 or more technologies. This is also the culprit that can make some technologies researched (or to be researched I just noticed) turn white rather than the colour they should be.

AI does not destroy/remove unused shipyards after it loses a planet/system to an enemy via conquest or culture flip.

AI does not understand that terraforming tiles around the Capital of a planet and surrounding it with factories/max manufacturing improvements is the best thing to do. (Retribution only, due to the RP bonus when capitals are leveled up). This seriously gimps the AI.

Gunboat-L (Small Kinetic) does not auto obsolete old designs.

There are 10 ships in that list so far, as the game progresses this list gets bigger and bigger, uglier and uglier

Extras:

Global Manufacturing Cost increase's or reduction's do not show up in any tooltip's.

Gaining a planet via one of the early game events does not count towards the required number of planets to trigger the Government pop up. (You can do it manually)

Coppied over from the Steam Forums, just incase