The odd notifications I remember are:
1) home world is being attacked (no it isn't)
2) energy reserves are low (at 300K+)
3) the AI telling me it's throwing something at me (but nothing is attacking)
4) the AI telling me that it has done something awful to me, like killing a command station (but it hasn't)
5) Human resistance arriving or departing (not always wrong, but occasionally)
I don't know if these are just delayed or showing up too early, I just know they didn't make sense at the time they showed up.