Getting to the surface is the last step of a safe ascent. Stop, breathe, think, and act is something that should be part of every certification agency's training standards. The dumbing down of skills is very worrisome.
Each in the buddy team should be watching and listening for proper assembly. Waiting until the diver has completed the assembly often results in only one person making sure of proper assembly instead of two or the group. How do two or more people result in a failure in equipment assembly? That is not a buddy check...
By immediately giving the okay signal upon coming to the surface, the person watching the entry turns around starts helping another. Do not give the okay until you are sure your are okay which also means that the person watching the entry is available to help if necessary!
Notice that you can see the diver's alternate 2nd stage keeper is not attached to his alternate. So... where is it?
Choosing a reg keeper that fails to keep the reg attached should be tossed. Find and use ones that keep the reg where you put it!
I teach, outside of demonstration of techniques, NEVER take the regulator out of your mouth until you are sure you have reached positive buoyancy on the surface. If for any reason the diver dropped below the surface, no water goes into the diver's mouth and can precipitate aspirating water. It also looks like the diver is not fully on the surface to be using his snorkel. His legs and feet are way to low to be “snorkeling.”
There is no control nor defense in the event of panic. The alternate should be donated and put in front of the face of recipient so that the only thing is visible is the regulator. If the recipient cannot see anything other than the donated reg, there is more control and doesn't put two divers at risk.
Additionally, this is NOT, “buddy breathing.” It is out of air and air sharing from an alternate. Buddy breathing is one reg between two divers! If the instructors use the wrong terminology, how can the students expect to do the right thing.
Additionally, he has a hand on the reg which looks like he is preventing it from being taken out of his mouth. One hand from each diver is enough to make sure they don't get separated. When he gets to the surface, he will have to find the low pressure inflator in order to orally inflate the BCD.
Since the donor has air in his tank and is letting air out of the BCD (because it is in his hand), it is possible that the donor could get to the surface and stay there and the recipient could fall away and drop back below the surface if he is let go of...
Cold air and cold water are the primary concerns. Cold water techniques MUST be taught if diving in a cold water and cold air environments. This is not an advanced specialty.
While there are aspects of each that have their merit and the pool is a great place to practice these skills, in the open water, doing these skills may have unforeseen consequences. The need to ditch ones weight, therefore easy access and understanding how of to do it, is important.
Similarly, removing life support equipment, namely the BCD with the attached tank and regulators has incredible risk. A technical diver would never remove their equipment and as the best trained divers in the industry, keeping your gear on has a valid reason. If one is on the surface and entangled, one can ditch their weights first and use a cutting tool to free oneself.