I'm not sure about that, par.002, but I've seen the placement.

Are you sure it wasn't a mining starbase and a normal one? I think the mining bases are an exception to the 3 space rule

Not only that, but the AI knows exactly where "habitable" planets are without every sending a scout... its pretty irritating.

That is not true.

The original poster's observation is true.  The AI uses a newer ruleset -- it can only build 4 starbases in a sector.  Humans don't have that limit yet.  We'll be switching to that in an upcoming build.

Oftentimes, what the AI will do (which I have started copying) is buy colony ships and just send them out in different directions. Just to get them away from your home worlds and out in space. That way, when you do find a colonizable planet, you likely have a colony ship closer to it than having to start from your home world. A few turns can make all the difference on whether or not you win the race to colonize.

You would think that exploring with your "builder" unit (i.e. Colony ship) would be pretty much the "standard-thing" to do...almost every 4x game supports this effective tactic. I'm surprised some people don't do this.

my flagship sometimes hunts down every anomaly in range, even if they're in unexplored space

That must have changed from the beta because my flagship wouldn't even stay on autosearch for the uncovered anomalies if they were more than a couple of sectors away.

I have been playing mostly tiny and small maps so far so I haven't used autosearch much in the current version. I use the flagship to scout and send my colonizers in the same general direction.

The AI loves those anomalies and will scoop them up while I am looking for potential colonies. For this reason I set the game to rare anomalies and let them waste time and money autosearching and building numerous scouts.

you can if it's in a different sector..

Ah, that explains it. They put an inluence base by my influence with only one space between them, but they are in a different sector.