After seeing this post by KapitenR (http://forums.galciv3.com/476469) I decided to try it myself.
I was playing as the Iconians and had the drone fighters due to the Paranoid Ability. I did not get pirates to attack any of my planets, but I did get the Space Monsters Mega Event. They attacked two of my planets several times, and I saw many of the same problems KapitenR reported. I did not check the diplomatic screen, so I don't know if they would show up there.
I watched every battle in the battle viewer and recorded most of them. The view in the battle viewer and the information displayed were usually very, very strange. Sometimes no information about any of the ships, mine or the monsters, was displayed, sometimes it was partial, and usually it was wrong. Sometimes my ships were not displayed, sometimes they were. Some battles seems to be completely normal.
Sometimes the planet turned invisible after the battle. It would come back after a few turns. Sometimes the planet stayed visible.
I eventually tried hovering over a drone fighter in the pre-battle view to see the stats and the game crashed like it did for KapitenR. When I reloaded the game and hovered over a monster ship, it did not crash. I then hovered over one of my drone fighters, and the game crashed.
Iconian Healing Ships Error
I was also reminded of an error in the Battle Viewer when an Iconian ship with Healing Hull is being attacked. The icons at the bottom of the viewer screen show the damage but not the repair. As a result, the ships are shown as destroyed when they have plenty of health left. Some of the videos show this.
Submitted Ticket #DFR-593-97193 with saves, videos and more information.