If you have two distinct sequences of events that don't depend on one-another, then consider it. If you have to write bunches of logic just to make sure that two operations aren't getting in each-others way, it pays off by making the two pieces of code clearer.
If on the other hand you find that, in attempting to make something multithreaded, you have to add gobs of code to communicate results between the threads, because one (or both) can't proceed without some information from the other, that's a good sign that you are trying to make threads where they don't make sense.
One case where it makes sense to go multi-threaded, even when you have to add communication to do it, is when you have one task that needs to stay available for input, and another to do heavy computing. One thread may poll for input from somewhere, blocking when none is available, so that when input is available it is responded to in a timely manner, and feed jobs to another 'worker' thread, so that processing continues at all times, not just when there's input.
One other thing to consider, is that even when a job is 'embarrassingly parallel' (i.e., requiring little or no communication between the parallelized parts), there are cases where multithreading may not be worthwhile. If your CPU can assign different threads to different cores, multithreading will give you a speed up, by allowing multiple cores to chew through the work simultaneously. But on a single core processor, or even a multi-core one with an unfortunate OS, having multiple threads will not speed things up, as the one core will still have to get through all the work.