I imagine their economy will shrink due to moving businesses, removal of cost-cutting centralisation, and not benefitting from the union's economic powerhouse in London. Tourism may be impacted too if you suddenly need a passport to go all the way up the M6/74.
The rest of the UK also loses out on North Sea oil, and footing the sizeable costs of separation (I'm sure the nuclear arsenal is just the tip of the iceberg). Just seems like a lose-lose situation for everyone really, especially when you consider that Scotland already has its own parliament and its MPs have powers at Whitehall.
But I don't think either side of the island's in danger of invasion. Who would do it? All our enemies are halfway around the world.
The biggest military issue it presents is for those poor Falkland islanders, as a divided British military would be a perfect opportunity for Argentina to finally make good on their threats and take them.
Also means Britain would have less impact on the global stage generally, with two isolated forces rather than one bigger, co-ordinated one.