Re: £350 million a week
Well only somewhat a con. It's actually £280m a week from memory. The £350m a week included our rebate, which by definition we don't pay - so was clearly deliberately misleading. But the argument was apparently we'd "have control of" the money - as our net payment is only something like £120m a week ish - that's the actual cash we get back. Though obviously we can cut subsidies to agriculture, which is about a third of EU spending. In fact that's DEFRA's plan, with payments for holding farmland to be phased out over the next decade and a (presumably smaller) amount to be moved to support maintaining hedgerows, bio-diversity and the like.
Sadly the quality of the referendum campaign was shocking on both sides - although at least there's some good organisations out there now to give you a better idea of what the true numbers are. I recommend Radio 4's More or Less - who covered this extensively at the time - and do lots of number checking at election times.
I'm not sure if the most depressing thing is the tendency for people to just pick numbers out of the air and shout them loudly, or the habit of deliberately misrepresenting the other sides' argument in order to make things even more unpleasant and polarised.
Why can't we all just get along, and declare war on France. That and tougher sentences for geography teachers are both sensible policies, for a happy Britain.