Air Law is the main problem.
I did the CAA PPL exams about seven years ago and have subsequently done the IMC and IR exams, but I am not an instructor.
All of the PPL exams can be passed, I suggest, by a fairly superficial reading of the book, some hours of good ground briefing and an intensive bit of work using the confusers.
However, passing the exam and understanding the subject is not the same thing. This is particularly true of PPL air law. Like most students, it was the first exam I took. I did it after a couple of months flying, when I knew very little about aviation in general and not much about air law in particular and when the hundreds of aviation acronyms were a source of confusion in themselves. I learned to pass the exam, rather than learned about air law.
Subject areas like VMC minima as opposed to licence privileges; special VFR; ATC services in different classes of airspace; documents to be carried; what is a release to service etc etc were learned to pass the exam but definitely not understood.
Some areas, I understood by the time I had finished PPL training; some areas, I only understood when I had finished by IR training. Some areas I don't fully understand now.
The danger is that, having passed the air law exam, the PPL student assumes he understands air law and never returns to the subject. Except for the gifted one or two students, he doesn't.
So, there is a case for a basic air law test covering only relevant parts of the syllabus to be taken pre-solo, simply administered by the instructor, perhaps. This would be followed by a second, more comprehensive, part and should be taken only after the GFT, when the aspiring PPL has had more experience and exposure to wider training and will therefore actually understand much of the problem topics which I listed above.
The fact that PPLs are confused by air law and the lack of real understanding is evident in many of the private flying threads and other flying forums. I say that, not holier than thou, but as a simple fact drawn from my own experience.
AA.