Which + Noun : is a noun following after which?
Solution 1:
"which complainants said had "infected and corrupted" the air" is a nonrestrictive clause that modifies "the problem of coal smoke". "Which" is appropriate for a nonrestrictive clause: https://owl.purdue.edu/owl/general_writing/grammar/that_vs_which.html . Using "that" would imply that it's a restrictive clause, which in turn implies that there are several problems of coal smoke, and you are specifying that you are talking about the one that people have complained about.