"I don't see it as my job to pretend for the captains sake that he has not forgotten something"
In my opinion that statement exposes a lack of understanding of human factors and a definate lack of finesse. You don't have to pretend he hasn't forgotten, but if you give him a chance to realise and remedy his mistakes before pointing them out the whole flight deck environment will be better, communication will be better and therefor ethe flight will be safer.
you are part of a team made up of two or three people. People are funny machines , they have personalities that interact, there is no doubt that some interact with each other better than others in producing a safe and efficient flight deck with excellent communication and S.A.
Imagine if your FMS was like that, get on well with it and it does a great job, be rude to it and it only tells you the bare minimum of what you need to know.....told you we were funny machines.
So it might not be laid out in black and white that you are to do certain things but that doesn't mean you can't show a little 'finesse' in your effort to create a safer, more enjoyable flight. Who knows, people might look forward to seeing your name on their roster as well.
PS it makes no difference whether it's left or right seat either, the courtesy/ airmanship flows both ways.