This past Sunday I was contacted by a recruiter to schedule a phone interview for later this week at 1:00 PM. However, she just notified me that the time will actually be 4:00 PM, because she didn't take into account that the interviewer will be in a different time zone (1:00 PM their time, 4:00 PM my time). Unfortunately, I have another appointment during that time, and cannot take the call without canceling the meeting. Is it appropriate to ask to reschedule for earlier in the day or a different day?
Yes, it is appropriate. Your recruiter does not expect you to drop all of your commitments at a moment's notice for a phone interview. Tell them you have a conflict that you can't get out of, and suggest some more appropriate times or dates as a jumping-off point for rescheduling. Any company worth working for will be understanding of this.