Yes, both good, although many would argue they aren't what they used to be.
Looking at the pictures of the socket backs, it's impossible to say with certainty whether the burnout was caused by poor quality socket contacts, or bad workmanship by the installer. Because they are unswitched singles, the terminals and socket contacts are joined directly together and heat flows readily between the two. Also, the burnt line conductor was pressed against, and melted into, the back moulding directly above the contact. But there are hints that the heat was generated by loose connections rather than slack contacts. Bad workmanship may well be the root cause, but there can be other factors such as excessive thermal cycling of the terminal due to the heating of poor quality, high resistance contacts.
Re. cutting off plugs, there is a UK-specific instruction that used to be standard, maybe it still is, I haven't noticed recently, advising users that if the plug didn't match their socket outlet, it should be cut off and destroyed, a suitable plug fitted and the correct fuse fitted in the DB. It's a hangover from the days when there were still some round-pin and non-standard sockets in use. There are still situations where that applies (clean-earth supplies in commercial buildings with T-earth variant BS1363 sockets etc). It would be ludicrous if removing and replacing the plug with one of the same type invalidated the guarantee, while fitting a different type did not.
Re. causes of plug heating, while all of Marconi's points are valid, in practice some of them are much more important than others and some can usually be discounted. The greatest variable, the contact resistance, trumps all the others under bad conditions.
Somewhere near the head of my list of things for the new video blog will be stuff about heating in contacts and terminals. In 1882, Musgrave Heaphy who wrote the first wiring regulations, the Phoenix Rules, was aware of how often bad connections caused fires. 136 years later we are still struggling to get to grips with this.