He's doing it right. There's a lot of things you cannot tell from the video, such as outside air temp, humidity, etc. The water temp he was using was about the same as body temperature, and is probably cooler than the shower you took this morning.
He's following the same 5 steps I use (degrease/detar, wash, clay, polish/glaze, wax). You can do the same thing he does using far less expensive products.
I wasn't too concerned about washing the car in the sun. The reason there is this "rule" about not washing the car in the sun is because the sun heats the metal or glass which causes water evaporation which leads to water spots. However, if there are other factors that prevent water from evaporating (e.g., high humidity or cool air temp), washing in the sun is ok.
Similarly, not using the so-called "two bucket" method to rinse his mitt was not a big issue because the car he was washing was essentially very clean to begin with. The two bucket method is beneficial for cars with at least moderate amounts of road grime and grit so that grime is washed away and does not act as an abrasive against the finish. But if there is no grit in the mitt or bucket, I see no need to rinse it. I've never used the two bucket method and I don't have any scratch or swirl marks on my car. That's because it never gets really dirty to start with so there is no grit/grime to cause scratching.
What concerned me the most was use of the pressure washer. IMHO, there is no need for a pressure washer under any circumstances when you're washing a car, and particularly those high-dollar cars this guy works on. A soft flow of water will rinse the car just fine and without the possibility of damaging the finish with high pressure.
