I think it is a load of bollox.. School is there to learn and to teach you how to learn. .
having a broad knowledge of things is relevant to life. . it can often show why were are where we are now and why decisions made now are made based on previous and historical experience and knowledge.It also makes people grow as they widen their knowledge in all things.
He mentions having a calculator so why does he need mental maths. Well sonny boy if you don't have a rough idea of the cost of what you've bought and what change you are going to get a calculator is a waste of time if you haven't input the correct numbers. The mental maths helps you know your input is correct and the calculator will just give you an more exact figure but, you should know roughly what it will be anyway.
The guy covers so much ground it's difficult to know where to start. Although I think he makes a few valid points I disagree with much of it and I think he's got some fundamentally wrong notions of what schools are for and the purpose of learning in general. I could probably fill up several pages with my thoughts on this, but as I don't have the time (and I doubt other FMs have the inclination to read it all 
), I'll break it down into a number of responses that I can post as time allows.
I'll tackle the mental arithmetic vs calculator argument first, as it's something that's been on my mind since the depressing sight of watching the HMs attempt the maths and spelling games at the start of the series. The argument that you don't need to teach mental arithmetic anymore because everyone uses a calculator now has actually been around for decades (I remember it cropping up on "Yes, Minister"), but I still consider it falacious. As Olly says, you still need to understand the basics of maths before you can use a calculator.
The "everyone has a calculator in their pocket" line has only really come true in the last few years with the development of smart phones, but even then - how many people get their calculators out to work out their bus fare, or the cost of their shopping? A lot of it comes down to having available a range of "tools" for different jobs. I work in a very technical field, so I need a scientific calculator. Something like 20 years ago I went out and bought the best solar-powered scientific calculator I could find, and I'm still using it. Admittedly I've tended to use my phone calculator more over the last year or so, but that's largely for convenience and I still sometimes use my "real" calculator because I like the feedback of real buttons and I find I'm less likely to make mistakes. I remember seeing an interview a little while back with Sir Clive Sinclair (who started off making pocket calculators, of course), and I was reminded that he famously still carries a slide rule around with him. His point is that there are some things (e.g. currency conversion) that can actually be done better on a slide rule than on a calculator. It's horses for courses...
There's also a wider general point (which I'll probably come back to later) that any learning can have unforseen benefits further down the line: although a particular subject may seem irrelevant in itself, it can form a building-block that leads to something-else that is relevant. Also there are the fundamental skills that you develop that are usually more valuable in the long run than the information itself...
yes that is sooo true. . What you learn formulates how you grow and think in the future even if at the time of learning it you think why am I having to study this. I immediately think of Animal Farm that we to study.. that taught us a lot of lessons for the future. . Lord of the Flies was another. .Merchant of Venice had a lesson to be learnt, as did Julius Ceasar and so on.. History which I personally hated back then is very relevant to us, it can teach us to maybe not make the same mistakes but, is also how we got to where we are now.
As you say maths is very important too and so many people don't even realise they are using it in their every day lives. Think recipes and measurements and add some science to that and knowing too much or too little of something could effect the outcome. All of the basics would have been learnt at school even if people didn't think they took it in or indeed needed it. Think betting shop and working out the odds, think handing over 20 quid for some shopping and knowing you have got the wrong change..
RE calcualtors, I did a statistics module as part of my degree and used a scientific calculator but, I then followed up with doing the equations by hand to double check the calculator result 
English Lang taught us how to formulate letters of all types, business, formal, friendly etc.. pretty sure that is no longer done anymore considering stuff I see nowadays 
What that idiot in that clip needs to do is learn, from having to learn as a kid, and go and research the things he claims he knows nothing about. errrm like what we had to do at school and in higher education too, research. Or ask his parents to enlighten him as well.. 