This is actually more a short piece of advise, a trip report rather than a question.
Last Friday I had a Edinburgh via Amsterdam Schiphol to Frankfurt connection all on KLM. The connection was displayed as such on the website and in all computer reservation systems travel agents use. The connecting time was 40 minutes.
Unfortunately due to air traffic control restrictions on a Friday afternoon we weren't allowed to take off in Edinburgh until 15 minutes past our scheduled departure time - and of course I didn't make the connection. It would have been the last flight to Frankfurt that day, so KLM had to book me into a hotel.
They offer great service to stranded passengers - but my advise to anyone is: No matter how highly people speak of Schiphol airport, don't book connections that are shorter than 90 minutes!