The works crapp, but it's salvageable. The first picture is a common way of doing joints; you cut it at 45 degrees, and then use a coping saw to follow the shape. In picture 2, outside corners are never easy, and often need filling, but he hasn't done that on either one, and that says a lot about his attitude. On the other pictures, it just goes from bad to worse, and is just shoddy workmanship.
You can salvage the work with 2 part wood filler, but you've got to rub it down before it goes off, otherwise you'll be at it for ages. The nail can be knocked in, and then filled, but it's the socket that needs the most care, as you'll need to switch the power off, and remove it before it can be worked on; and unless it's removed, you'll never get a good finish around it. The second to last picture should have been taken up to the moulding, and then chamfered across
Part of the problems, is that it's MDF skirting, and that'll never get as good a finish as pine does, but he should have tidied up the gaps that he's left, and not leave them for the decorator to deal with.
You're real question, is do you want him to redo it, or would you rather get someone else in to sort it out, and then take their costs off of his bill plus a bit more for your hassle - he's entitled to something after all. As you've suggested, if he gets stroppy, tell him you'll be happy to put his work on facebook
