This is what I'd love to see from Espionage. A special "espionage screen" all it's own, broken down by races not unlike the Races screens. On this screen you can see not just what ops your spies have carried out, but strategic decisionmaking information from the AI of that race, plus information about their technology and ship designs.
Bear with me. This takes a bit of explaining.
It occurs to me that the AI in GalCiv 2 makes strategic decisions, based either on randomness, racial preference, or the actions of other civilizations. For example, at the game outset, a given AI may decide to develop shields and mass drivers. Why? Why not? No one's really started an arms race yet, and you have to start SOMEWHERE. Now, as things stand, you can get an idea of the techs they've developed through the dialogue screen or the tech analysis...but you don't know what they're doing NOW.
I'd love it if you have Espionage at a certain level, you start getting info about the AI's decisions. Something like, "The Drengin have decided to develop missiles as their primary weapon!" Or, "The Drengin have noticed our specialization in beams weapons, and are developing shield technology!" Maybe even updates like, "The Drengin have ceased producing colony ships and begun mass producing warships," or "The Drengin are planning to attack our colony at Ceti Alpha Six within ten turns!" Again, at sufficiently high espionage levels. The more you have, the more of the AI's mind you can read.
Similarly, when the AI develops a new tech, or designs a new ship class, warnings about it could be found in your Espionage Screen...ranging from vague (The Drengin have designed a new attack craft) to specific (The Drengin have designed the Cruiser MX01, which has a Beam Attack of 24 and a Beam Defense of 6)...depending on Espionage level.
Maybe it's just me, but it seems to me that it would be a great way to encourage espionage (maybe introduce counter-espionage, that inhibits how much the enemy learns?) and make the whole thing vital to outguessing the AI's strategies, rather than an intriguing but ultimately negligible novelty that it seems to me to be at present.