Yeah, there are a lot of problems with this episode. As an allegory for terrorism and radicalisation of people within our own society, it was heavy-handed at best. And as a believable set-up, it simply wasn't - this is the "totally watertight peace treaty with safeguards built in for both sides"? Settle twenty million shape-shifting aliens amongst the human population and hope that nothing goes wrong?
For one thing, how does that even work? The Zygons have supposedly been learning new tricks since they arrived, but as the Doctor said, up until that point the only way for a Zygon to maintain a human form was to have a living human to imprint from. So were all these Zygons duplicates of already-existing humans, and what happened when one of those humans died?
Also, the original-series story that introduced the Zygons made a major point of them having some very specific dietary requirements - they needed the milk of a bioengineered creature called the Skarasen, a large amphibious beast that happened to live in Loch Ness. Does this current crop of Zygons have their own Skarasen, and even if they do, how do they manage a Skarasen-milk round for twenty million undercover aliens?