When you move your ship to some place far away, and then gift them to another race, the "cleared" area of your ship's original sensor remains visible forever.
The same thing happens if you have a ship done in a planet for the next turn (bought, say), but after you press the "turn" button your planet is invaded and the said ship magically disappears. you also have "eternal vigilance" on that planet
in the domestic page, the sliders that controls military / socal / research do not work very well. try locking one and moving the other two, for example. often they would end up visually set at the same place but with a distribution 15% 30% 55% or something vastly different
if you build a fast ship (but have no attack / defense) you can lead the AI fleet in a runaround, and it never catches on - or none that i notices.
in the single player campain, i assume it's not possible to do trade for the first few missions - nonetheless, the quartely report keeps talking about we need to research trade, etc. if such technologies are not available for a mission, please clearly indicate so.
probably more "enhancement" than "bug" - the research / build credits really ought to spillover to the next project - ala Civ4. this, combined with the not-very-functional sliders, make it hard to control overheads in this regard
it is also not possible to turn off a specific type of spending per planet. while the spending can be concentrated, it is wasteful for those turns where a "faster" planet already run out of social projects but is still spending like 20 on social despite the focus is on military. is this a design consideration? at least make these "wasted money" go toward the bank, or "toward morale," "toward influence," etc (i don't need to say "ala what" right)
by the way. this is all with 1.0X