What are the possible weaknesses of this peer approach to valuation?

The approach does not account for industiy context, the company might have multiple divisions, and the approach focuses on the statistics of only one company.

The chosen peers might not be true competitors, the company might have multiple divisions, and the most appropriate competitors might not have P$/$E multiples:

The chosen peers might not be true competitors, the approach focuses on the statistics of only one company, and the most appropriate competitors might not have P$/$E multiples.