Here are several issues that cropped up in the late game (about turn 435 or so) with large galaxies. These issues came up with two different single player games. The first game I played Terran with a single, Drengi AI opponent. The second game I played Drengi with three AI opponents. Both large galaxies
1. Ships no longer deal damage
Both my ships and the enemy ships would not longer deal any damage to each other. If I saved the game and tried again, the ships would deal damage for a turn or two, then no further damage would be dealt. All ships essentially became invulnerable. The only way to proceed to victory was through planetary invasion.
In some game, saving the game did not effect this bug.
In one specific case, a gunboat ship attacked a defenseless transport multiple times, but did not kill the transport.
2. Some ship paths are rendered as very thick slashes across the screen
This issue must be a rendering issue. When a ship was given orders to explore, the game rendered one of it's path "ticks" extremely large so that it subtended a major fraction of the game screen, even when zoomed out to maximum. Sometime the big "tick" was permanent while other times it would flash on the screen and disappear.
3. Game crashes
When the above issues manifest themselves, hitting "turn" will cause the game to crash. As soon as "turn" is hit, the game music begins to stutter and several of the animations also stutter. The game then crashes hard.