Great stuff, but there are mistakes. At least I think there are mistakes!
The people of Northern Ireland are not called Northern Irish. Those who are Roman Catholic are called Irish; those who are Protestant are called British. Northern Irish just isn't used! The official term is I think "people of Northern Ireland".
What's this about Isle of Wight, Anglesey, Hebridies, Orkney and Shetland being outside GB? I suppose they are outside the geographical concept of GB, but there is also the political concept of the GB (The UK of GB and NI) which certainly includes them. Indeed the clip seems to think that GB is a geographical concept alone - it is both geographical and political and the two don't exactly overlap.
I don't think the four home nations can be called "sovereign nations". The sole sovereign state is the UK, which is the sole authority which issues bonds and which has a unified foreign policy. The issue of the home nations does need to be explored. England and Scotland are kingdoms; Wales is a principality of England (and therefore doesn't get to have its flag on the Union Jack). Ireland was a kingdom; the territory of NI is not usually so described but as far as I know is constitutionally still a kingdom.
The clip doesn't examine British Antarctic Territory.
The clip ignores the usage in sport. Often the island of Ireland is considered to be a single "home nation". The clip ignores religious boundaries. In the island of Ireland these cross the political border. There is a diocese of "Gibraltar in Europe".
The clip also leaves out 101 areas of complexity around the heritage of empire. In most cases we have structures which would permit the rejoining of former parts. There was a call before Christmas (from Ian Paisley, Lord Bannside) for Ireland to accept "reunification under the crown" as a solution to its present problems. I'm well aware of the issues this would pose in Ireland, but as an issue in UK constitution such reuification would be very easy to bring about.