I wish all my customers were as easy going as the OP.
Seems to be a very decent and forgiving person.
I doubt if I would get away with that work for many of my customers.
Well, unfortunately it's not that simple to just sack someone and find an alternative when your bathroom has been ripped out and you have a family (with two kids under the age of 3) to think about. The time it takes to get a quote and find someone with availability in the area where we live would delay things by several weeks or months.
But I think the main reason I come across as forgiving is because as a customer, with very little to no knowledge of plumbing, I don't feel qualified to criticise work done by someone who is supposed to be a professional plumber. The only reason I was confident about questioning the waste pipework was because gravity is something everyone knows about (apart from our plumber it would seem!!).
Also, the suggestion to rip out everything he's done and start from scratch won't address the problem with the notches and holes not complying with building regs, so provided I can make sure there is a fall from the basin, what is there to be gained from starting again? Granted, the wastes could all be kept separate if everything was redone, but that would mean cutting more holes and weakening joists even more, so not ideal...