It can be a challenge, especially if one or both people have limited computer-time. For example some of the teachers I've looked at early on were 'ruled out' simply because of time difference - they didn't have enough available time slots when I'm available. And at the moment as well -  I have a teacher I only meet on weekends, once in a while because otherwise our times don't overlap much. 

It's really a big problem. I am completely "out of use" in the evening. I have to take lessons in the morning when I can concentrate. Fortunately  now my teachers live (more or less) in the same time zone, but some have jobs during the day (besides Italki) and are available only in the evening so I had to renounce and find someone else.

It's hell! I am spending some time in Ukraine now and timezone in Europe is horrible for me because most of my students are americans and they're not willing to have early morning or very late evening/night lessons (which would be my mornings and afternoons because I also don't want to work after 6pm or 7pm) and it's also horrible for European students because in their jobs they don't have much flexibility like Americans (many of my American students take lessons in their offices) so my European students also would like to have lessons after 6pm and I am not that willing to teach that time. So yeah, pretty much Europe timezone is a headache for me but for obvious reasons it is great for my language exchanges since I am learning Russian and I'm in their territory :D~

Yes, it is a problem for both of us. We are living in different rigions in most cases. If we want to have a conversation online, we have to make sure that both of us have free time.