> Seems surprising that they have to sell the whole Motorola division for less than they bought this little company Nest for.
At the time of the Motorola acquisition, it was widely portrayed that they were buying the patent portfolio and that the rest of Motorola was largely dead weight that came along with the patent portfolio. Since they are keeping the patents (but giving Lenovo a license to them), it doesn't seem like that bad of a deal.
As for why Google specifically acquired them? Possibly because a general partner at KPCB (Nest's biggest investor and one of Google's early investors) also holds a seat on Google's board. Nest was one of Google Ventures largest investments and Google Ventures holds a seat on Nest's board. There's nothing like having the seller also be the one involved in the buying decision.
Nest makes great products and has an awesome team. I think they're worth more than what Google paid.