I have to agree about the coat. Spike continuing to wear it after he knew who Robin really was could be considered bad taste. Unfortunately, that coat has been established as being as much an integral part of Spike as Mr Pointy is to Buffy, so just tossing it would have been bad, as well.
As for Robin's justification in trying to kill Spike, it's no more valid than Holtz's vendetta against Angel because Angelus killed his family. Understandable at first, certainly, but if we have to accept the fact that Angel is a character different from the soulless monster known as Angelus, therefore not responsible for Angelus' crimes, then we have to allow Spike the same consideration, despite the lack of name change. Buffy tried to explain that to Robin, but he simply refused to accept it, exactly the same way that Holtz refused to accept the same thing about Angel.