A big challenge for Eve players is the fact that, due to the single-shard nature of the game, players come from all over the world and thus have all sorts of different playing schedules.
I can't comment on the effect this has on, say, null-sec warfare, since I don't have a clue about it, but I know that for RP it can be quite a challenge to come up with a) compatible times for a group of geographically disparate players but also b) plausible IC explanations for why your character misses the events they do, goes weeks without talking to a particular character, and so on.
I suspect this has a bigger impact on people in less populous (eve wise) time zones. Like, er, mine.
I tend to suggest in my blog and RP that there are indeed timezones in Eve - that different stations, for example, might be on different local times - and also that there are a variety of 'shifts' people might work. (I've heard the 'shifts' explanation from other characters in RP too).
Neither of these entirely works for me as a complete explanation. After all, Cia is an independent and wealthy pilot. If she wanted to run her operation on a different clock, she could do it with a click of her fingers.
I try to manage some of the contradictions by assuming that Cia does a lot of things when I'm at work anyway: OOC contact with players on agreed events that might happen when we're both off line fills in some of the gaps in Cia's life ('So, let's say our chars met up for a drink after work? Cia's had a haircut, btw. Oh, and she'd probably mention that guy she's seeing.') but I know that hand-waving such 'off-screen' stuff doesn't work for everyone.
How do you handle timezone problems?