What was one shortcoming of alpha zero that Kasparov noted? I [Kasparov]  can look at AlphaZero’s games and understand the
  potential weaknesses. And I believe it has made some inaccurate
  evaluations, which is natural.


The reason he says that is AlphaZero uses statistics of ALL games to determine piece value.  

Which pieces did he specifically mention?

What other shortcomings does alpha zero have that humans could exploit?
First, as great as Kasparov is, compared to AlphaZero, even he is a patzer; so for him to say that he sees weaknesses, he may be correct, but it could also be, simply, that AlphaZero is playing at a level beyond even his great understanding, and with positional/tactical minutia we, humans, have yet to realize are important, or cannot see at all.

In this interview, he only mentioned bishops versus knights, saying:


  I can look at AlphaZero’s games and understand the potential
  weaknesses. And I believe it has made some inaccurate evaluations,
  which is natural. For example, it values bishop over knight. It sees
  over 60 million games that statistically, you know, the bishop was
  dominant in many more games. So I think it added too much advantage to
  bishop in terms of numbers. So what you should do, you should try to
  get your engine to a position where AlphaZero will make inevitable
  mistakes [based on this inaccuracy].


Note: I believe the 60 million games he mentions are all games played against itself as it was teaching itself how to play, rather than a database of human games. After all, Mega 2020, has only 8 million games in it.

I also found this article that Kasparov penned, in which he said:


  But in my observation, AlphaZero prioritizes piece activity over
  material, preferring positions that to my eye looked risky and
  aggressive.


Considering the recent question, "Is Stockfish 11 (level 20) beatable?", and that AlphaZero destroyed a recent, although previous, version of Stockfish, I do not believe that you will find any weaknesses that any human will be able to exploit. That will be the domain of the next, stronger, computer.