In just one game on a random 4 player map on Unfair difficulty I encountered all of these in one sitting, so I imagine they can't be too hard to reproduce. I kept telling myself I'd save the replay and then totally forgot once the game finished.
Sometimes when ships are told to go to a planet they will and then turn around and immediately go back to the planet they came from. I had an asteroid and the enemy had a desert planet I had been trying to siege, when I finally took it and told all my ships to move up that planet they'd keep juggling themselves back to the asteroid before I finally gave up and scuttled them.
When telling ships to retreat there was a number of times a few of my capital ships specifically would refuse to retreat. Other ships had the same problem but to a lesser extent.
Capital ships will still colonize a planet and then it'll follow up, sometimes, a few seconds later with the planet being uncolonized. This was still present in 1.03 so it wasn't specifically 1.04 that caused this one.
Colony capital ships will not colonize a planet automatically a good portion of the time.
Capital ships will sometimes ignore bombing planets altogether. Even when they would bomb they would wait until absolutely everything was out of the planets gravity well, fighters and bombers included.
AI will not build another frigate factory if you take out the last planet they have with a frigate factory on and they have no available logistics slots on any of their other planets. I took out one of the AIs home world and took over the next 4 planets of his with no resistance. Looked at his last planet and still, nothing. Left that last planet alone for the rest of the game, which took about 7 hours to finish, then went back there to check on it and still nothing.
Not a bug really but an oddity. One of the AIs kept sending small skirmish parties of roughly 15 ships into my colossal fleet of roughly 100 ships until he drained absolutely everything he had. So far to the point where he'd send in his level 10 capital ships, one by one, until I had killed every single one of his capital ships. At first I thought this was a clever ploy being used but then targetted all his planets to find out if he was up to something else but no, he exhausted everything he had.
I can't say I'm too happy with this. This is making the game almost unplayable when ships ignore orders and the AI refuses to put up a fight, on unfair no less. The (listed) changes that were made in 1.04 are great however. I just hope things like this get dealt with in 1.1. *crosses fingers*