Confusion about special and general relativity accounts for almost none of the problems that programmers encounter in practice. If that's your use case, then fine, time is special and tricky.
The most common issue is a failure to separate models vs. view concepts. e.g. timestamps are a model, but local time, day of the week, leap seconds are all view concepts. The second most common issue is thinking that UTC is suitable to use as a model, instead of the much more reasonable TAI64. After that it's probably the difference between scheduling requests vs. logging what happened. "The meeting is scheduled next Wednesday at 9am local time" vs. "the meeting happened in this time span". One is a fact about the past, and the other is just scheduling criteria. It could also be something complicated like "every other Wednesday", or every "Wednesday on an even number day of the month". Or "we can work on this task once these 2 machines are available", "this process will run in 2 time slots from now", etc.