Just finished a USA game, here are some notes
-The Texas war of independence will always result in white peace. In fact, the armies of both countries are just standing on their home soil for a couple of years (at first I thought that this was caused by me adding Texas to my SoI and thus Mexico feared me intervening, but tried it again without me influencing Texas with the same result). Moreover, in one of those tries I inherited Texas while they were still at war with Mexico (see screen below) which doesn't make any sense really.
-Somehow I felt that the +2% bonus troops give you when colonizing doesn't apply in 1.3 -or at least it is way too slower than in 1.2. In fact, Mexico colonized Colorado before me, even though I had troops there and the AI had none and they started colonizing a month before me.
-I had the already mentioned issues when recruiting brigades until ca mid 1880's.
-After winning a war against UK for a Canadian province the UK would have at most 5 brigades guarding Canada for the rest of the game -before the war their army there was at realistic levels, unlike 1.2 version where they would have something close to 500,000 soldiers there. Even worse, every 5 years they would declare war to me and would only use those 5 brigades to attack me, without sending reinforces. On top of that, after innevitably losing the war, they would immediately attack France with the same method and lose again.
-The war score needed to acquire any non-core province from Mexico is too high imo (I think one province even requires a 109 war score)
-Late in the game my government switched from intervensionism (democrats) to laisez faire (republicans). While democrats were on office I'd pay ca 100$/day on industrial subsidies for various factories. With the subsidies gone though only one factory was closed which I think is a bit unrealistic. Still, laisez faire works extremely better now than it did in previous versions.
-The AI would honour its alliances 99% of the time.
-Austria will always attack Denmark for S-H, unlike Prussia, which doesn't make too much sense.
-At some point France was #1, but in the end UK finished on top, with me second.
And a couple of suggestions for a next patch
-Lower the military score gain from dreadnoughts (I think now it is 20 points/ship)
-Add a remove core war goal and a "proclaim guarnatee" option
-Perhaps add a penalty to the industrial score of provinces who are not at the same geographical region as the home country. I don't think it is realistic that a level 5 cement factory in India is as significan as a level 5 cement factory in Manchester for example.
That's all, sorry for the long post.