The way the student was allowed to conduct the take-off has already been covered. Myself and many other instructors have probably done this on thousands of occasions without incident, with good risk management and vigilance it is no more dangerous than when they enter the circuit later for take-off and landing practice.
Second the motion.
Finally the stall, use of controls near the stall should be coordinated. The report seems to indicate only aileron use until stall was identified then the use of rudder. The initial roll to the left sounds like it was student induced, the sharp roll right was probably linked to stall. Using aileron only to stop the right roll at that point would have caused sharp adverse yaw and led to the situation the instructor observed, I have seen this many times during stalling in 150/152 where students insist on using aileron only to roll level. By the time he was instigating the rudder the nose had already dropped and rate of descent was beyond recovery.
Tip for newer instructors having difficulty with this;
In a benign handling aircraft such as a 152 or 172, a good way to encourage the use of rudders over aileron to the student is to hand over the rudders only while holding the aircraft into a fully developed stall. Get them to initially start steering the aircraft gently to the right or left, then back the other way. A tommyhawk would be a bit aggressive for this, but sometimes it takes a seeing is believing approach. Discuss with your CFI.
For the dickywhackers who want to jump on the "that's not how you recover" bandwagon, this is only to lead the student into using rudder to ARREST FURTHER ROLL.