This is a very good question but the problem is, is it a good idea? Will it make your partner appreciate you more or start having some form of hatred for you?
All these rhetorical questions can only be answered through experiences of trying them out cause people differ, some might appreciate it while others might feel inferior hence wanting to create a scene.
Some people will get really annoyed, whereas others may actually want to be corrected.
Try correcting them once and watch thier response. If they get annoyed, don’t do it again.
But if they seem fine with it, then ask if they would mind if you correct thier grammar once in a while and tell him that he’s welcome to correct your grammar as well!