Thermodyamics would suck. you have to put plenty of insulation, which would cover up everything, which would defeat the fact it looks like a Lego house.
unless there's tranparent insulation?
They built the Lego 'bricks' around a timber frame. Although the Lego was structurally independent to the timber frame, the timber would provide structural support if the Lego structure failed.
I would have thought it would be very simple to pack between the Lego / timber noggings, studs and joists with Rockwool insulation. If you were fastidious in the application of the insulation, you could prevent cold bridging. The problem would be with the windows because they were made from transparent Lego pieces.
Additionally, you could coat the liquid pieces in a liquid waterproof coating to make the structure waterproof or glue each Lego piece together. Then water test the whole lot to identify leaks. This would also strengthen the structure.
However, the above goes against James May's philosophy that the whole house could be taken apart (you should see the scenes in the show where they were experimenting with making Lego load bearing beams and floors).
Edit: Just noticed that they have missing sections in the wall to the front of the house; I suppose you could count this as the trickle ventilation to the house