I'd say that 'that said' and 'at the same time' are used to introduce a caveat, a contradictory idea, one that goes in the opposite direction and flips the intent of the original sentence ('It's a risky operation' suggests resistance to the idea; 'that said, it could be very advantageous' suggests the speaker now supports the idea).
'With that in mind' acts as a bridge between an argument and a conclusion (or plan of action). (Eg: 'I don't understand Danish and I've never been to Denmark. With that in mind, I've decided not to accept your job offer as a tour guide in Copenhagen.') What follows is not usually an opposition, but a logical conclusion. (I think... )