+1 to that, I haven't seen any noticeable lag due to the number of ships. Turns can take a little longer by a second or two or something, but otherwise no appreciable lag.
Re game slowdown in general, I have noticed some lag in late game, particularily if you're conquering the whole galaxy and it's more noticeable there when there's fewer civs alive. But that seems to be independent of ship number and is more the 'late game slowdown' curse that affects all 4X games. Though some have a better handle on it than others.
I am noticing the AI races are spending a lot of their construction on ships to beat the critters, but they never seem to destroy the shipyards/nests. Maybe tweaking the AI a bit to actively destroy those is needed?
Yea, I've noticed that the AI has a serious problem with cleaning up shipyards. Planets with shipyards from two factions are somewhat common and I've seen ones with three shipyards, but those are less common. Nvm, I thought you meant major civ shipyards. The AI does eventually clean up the hostile shipyards (unless they're Xeloxi), though there's always that one sector or two that has difficulty cleaning things up.