Are there things that one shouldn't be mindful of?
Yes there are. Being mindful of "signs" that turn the mind to anger (or lust etc.) is unwholesome. E.g. someone irritates you and you insist on attending (upaṭṭhāna) to that particular experience (a product of your mind!), instead of focusing on something more positive.

Mindfulness in and of itself is a neutral factor of feeding, the question is what you feed.