Another part of the problem. It sounded like the student wasn't writing down his clearances as he went along. Since he was having trouble keeping them straight in his head, he should have been, listening-writing-reading back-moving.
That helps me, although I can't always take the time to do it (and it isn't always necessary).
Radio comms, especially if the other party is talking fast or you're nervous or unfamiliar with the phraseology, can be tough to master. It always helps me to write down what was said. Not verbatim - just the nuggets to make a string of pearls that will help me to make sense out of a foreign language. The more you do that, the more everything will make sense and shortly you won't need to do it any more. Aviation talk is a different language with its own sentence structure and words. The only way to become fluent is to stumble your way through until you eventually get to the point where you don't have to think about the pieces and parts of what you're saying and you can focus instead on the information.
Timing is everything with taxi instructions. I had just touched down on Rwy 22 at KJVL last year, and tower said "Cessna 61A, left on Charlie, left on Alpha, cross 18 to Alpha 1A."
I was still rolling at a good clip, and certainly didn't have my airport diagram in my hand as I was still slowing down, so when I turned off on Charlie, I must have sounded like the kid in this thread when trying to read back my taxi instructions, as I didn't recall half is what he said.
Fortunately, after I was on C, I stopped, pulled out my diagram, and used Bob Gardner's famous "say again?" All was then well with the world.
When I was a 5 year old boy we were stationed in Naples. I didn't know a word of Italian, and Neapolitans can't say a single word without saying 200 words real fast. For the next 4 years the only words I ever needed to say to get me out of a jam was "Io non capisco". Worked like a charm. Suddenly the words slowed down, gestures became more expressive and understandable, and information could be exchanged and turned into knowledge.
In my opinion the CFI and student were both at fault. Either of them could have fixed this situation if they had only stepped up to their responsibilities. But neither the CFI nor the student fixed their issues before this flight, and so by the time this recording starts the only person on the planet that had the experience, the ability and the responsibility to make the best out of this bad situation was the tower.
Tower knew that this pilot wasn't comprehending the words that were being said. For reasons that we don't know and weren't relevant by then, this pilot wasn't able to follow simple instructions on that day. So knowing that people die when pilots do stupid things, the tower should have exercised his greater experience and his vastly more capable understanding of the situation and dialed down the drama. I'm sure he would have loved for this pilot to understand and comply with his instructions, but you deal with people where they are - not where you want them to be. There's always time to humiliate and berate people later - as in after we get the mentally impaired guy in the dangerous machine safely parked and away from areas where he is a danger to himself and others. But right then wasn't the appropriate time to indulge in some student bashing. It obviously didn't help anything at all.
It feels good to intimidate others. It makes you feel superior when you point out their faults. That obviously wasn't working in this situation, and yet the tower never changed his tone or the way he approached the problem. The sad thing is that this tower guy probably retells this story to his buddies over beers and everybody gets a great laugh out of it, and he'll do the same thing the next time he comes across a student that is obviously in over his head.
It reminds me of American tourists overseas that believe that repeating the same words louder and with more feeling will somehow miraculously make them more understandable.