I was curious as to whether playing a fast or slow game had an affect on the difficulty of reaching certain paths to victory. It seems to me that Science and Culture victories would be much easier on slower games. I know that research times and build times scale, however; I was thinking perhaps that the scalability is not perfect.
I've been playing "fast" games to get the "Master of the Universe" achievement recently, and I haven't found that Science or Cultural victories are that far out of the question. A science victory can take a while (you might get down close to the end of your turns), but it's not impossible. Cultural doesn't seem that difficult at all, honestly.
Diplomatic victories are mainly won by influencing city-states, from my experience, and this is no harder in a fast game than in a slow game.
The one that might surprise you is a military victory - in a fast game, you've got fewer moves before your units are obsolete, and everything ends up being further apart in terms of the turns it takes you per unit time to move. This is kind of balanced by the speed at which you produce units, somewhat, but it still seems like it would be problematic to fight a war with a distant enemy. Against many other Civs on a large map, you'd probably be much harder pressed to win within the time limit.