Can I see how many mission items I've found during the current mission?

You can't see it in the menu or anywhere else. The only things you see is:

  • If you find one collectable, it will display your total amount of collectables from this type in the bottom line.
  • If your done with the level, it will provide a summary of all found collectables and those which could be found in the level.

But you can take a look at a list of collectables per level to get the info early enough and just remember how much you already found in a specific level. Such a list can be found here.