In a casual game, I will always remind opponents of any effects I remember myself. I extend this, depending on the experience level of my opponents, to things like, "There's no reason not to spend your Focus token, since you know I have to shoot this guy" or "If you Barrel Roll left, the Boost right, you'll get out of my arc and still be able to shoot at me."
In a tournament game with little at stake -- e.g., pretty much any game below the finals of a Store Championship -- I'll do the former (remind them of any effects I remember myself), but I generally only give advice on tactics to new folks in these games (as teaching, and encouragement to keep coming back).
In a high-level tournament game, I always remind opponents of mandatory effects, and will apply them at any point necessary that isn't precluded by a changed game-state. (E.g., if we forgot Stress from Captive, but a ship has moved in the next turn, it's too late to apply it. It might not otherwise be too late.) I only remind high-level opponents of permissive effects, frankly, if I'm easily winning.
As a spectator, if I notice something mandatory being missed, I say something, and I strongly believe that is the responsibility of every player-spectator. On the other hand, I never mention permissive stuff, except in casual games, and I also think not mentioning permissive effects is the responsibility of player-spectators.