I had my first experience with AI autoplay during one of my games and thought I'd share the experience in case others were contemplating the same... this is a very useful mod for some things, but it should be used with care in other situations...
In my case, I wanted "cruise control" for the 37 turns after I launched the spaceship (betterAI 0.37 / 18 civs / Huge map / Marathon speed)... I was playing as Shaka and was first in land, but only half as powerful as Hatty, who was playing a quite a war-monger game... but she was pleased with me, so not a big deal... right?
I gave control to the AI for 35 turns, but I noticed several things that made me nervous...
1. Hatty immediately went from Pleased to Annoyed as soon as the AI took over... it closed borders, picked a religion (I was Free Religion), and switched civics... actually the civics switch was the most bone-headed move of all... I had over 40 cities on one continent, controlled two holy cities, owned the Statue of Liberty and Sids Sushi... perfect formula for Representation + Free Market + Free Religion. I had fish trades with every other AI on the map. The AI picked Monarchy + Communism + Theocracy and canceled all fish trades... many of those were quite lucrative even in Communism (my spices for their fish & 12 gold)

... my GNP went through the floor... OK, who cares about GNP after you launch the spaceship, but this completely cratered my relationship with Hatty, who had "Too much on her hands..." when I checked 35 turns later.
2. Further adding to the economic insanity mentioned above, it crammed 10 or 15 new cities into places I'd rather it not (i.e. encroaching on my uber-powerful Heroic-Epic city).
3. I usually organize my troops into stacks... C3+CR3 maceman upgraded all the way to Mech Infantry go here; however, the instant I gave control to the AI, those units sprayed all over the map.
4. There is no pause functionality... I'd like to have time to see what the AI is doing in a given turn... but these turns go by so quickly, it's really hard to know in detail.
In a perfect world, we would be able to give partial control to the AI... and have selectable options so I can pause it at any given moment, can't touch my 100-unit war stack, can't switch civics, can't cancel existing deals, can't build new cities, and automatically reverts control to me if someone declares war on me. I realize this may be a tall order, but if it is going to fill the need as a cruise control in these kind of games, I think these things are very useful.
Thanks for all the work so far, this is an awesome development mod... but at this point I'm a bit nervous about letting it finish anything but total war-monger games.