In general, listen to whether it sounds good or whether it has something that irritates you. Or whether the sound is fitting or whether it's e.g. weak (in the modern days of dynamics squashing that can be a valid notion that you may want to adjust with compression. Just remember what the dialogue is for, i.e. it has to sound humanly like the person who's speaking it and it has to be intelligible, so all processing should aim to be rather natural and focus on clarity and minimizing any sort of irritation in the sound).
Ideally, dialogue processing doesn't need anything more than some EQ, some gain riding (prefer it to compressors, unless you're in a hurry, although modern vocal specific gain ride plug-ins can work really naturally) and a compressor/limiter to finish it.
But, dialogue can and preferably should be recorded, to save yourself from headache, so that you may not need to do anything but cut and add some fades, and possibly add a very small amount of sweetening/finishing EQ (or compression). I.e. the dialogue should sound almost, if not totally finished already when recording. In this approach having a good and carefully selected microphone is essential, the placing and micing angle has to be correct, the actor must attempt to/be able to speak/sing consistently (i.e. consciously keep the dynamic range that he/she uses under control. Or, you need to adjust the microphone according to how loud or soft the actor's dialogue goes.), his/her voice obviously has to sound good, the recording room must sound neutral and you must retake and readjust everything that doesn't sound good enough. In location dialogue recording controlling the environment and the mic positioning becomes an art of its own, which is why they invented ADR though.
So, don't spend too much time wondering how to post-process the dialogue. Focus on making the recordings as good as possible, and you'll need to do less later and it will come out sounding better.