In the Harry Potter universe, wizards and witches have managed to keep Muggles unaware of their existence, across the planet and over many centuries. Up to the timeframe that the novels take place in (the 1990s), I can see how this can be achieved through a combination of discretion and magic, with discretion being the preferred method on occasion (e.g., you don't need magic to slip into Platform 9 3/4 unnoticed, you just need to check that nobody is looking).
Our current world of 2016, however, its a very different place. The UK is (in)famously heavily camera-monitored (an estimated half million CCTV cameras in London alone). Even more poignantly, a very large (and growing) segment of the population carries an internet-enabled HD camera with them at all times and are willing to use it at a moment's notice (this is comedy, but it is comedy in part because a more realistic version could happen). It looks like, the moment something magical happens in public, a video of it would be on Youtube/Facebook/Twitter and within minutes.
How does the Ministry of Magic deal with this development? Do they need to create a dedicated corps to monitor social media services and alter records as necessary?