Strange case: Bottle of water freezing

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Cool demonstration but not a mystery much: I think it is just supercooling. The lack of imperfections etc. provides a lack of nucleation centres.

Shaking does the rest.
 
I think you are right...I no idea water could be supercooled to such a LOW temperature:
Water normally freezes at 273.15 K (0 °C or 32 °F) however it can also be "supercooled" at standard pressure down to its crystal homogeneous nucleation at almost 224.8 K (−48.3 °C/−55 °F). [2][3] The process of supercooling requires that water be pure and free of nuclei such as having undergone reverse osmosis, however the cooling itself does not require any specialised technique.

http://en.wikipedia.org/wiki/SupercoolingI'm also surprised because reviews of bottled water show it often of a no so good quality...Consumer Reports, I think.
 
Exactly, it is due to the lack of suspended solids and gas bibbles to act as nucleation centres. Overheating is also easily observed if you heat water twice in a microwave oven. The second time due to the lack of gas bubles to act as seeds for condensation you can reach a temperature much above water's boling point without boiling, however, any disturbance causes an explosive generation of vapour (if you decide to try it, be very careful!).