What is the best way to alert Elsevier or Clarivate Analytics -- for instance, if I see a potentially predatory (or just really low quality) journal indexed in Scopus or WoS or if I see recent changes that possibly indicate a lowering of standards by the journal (such as a dramatic increase in the number of articles published)?
First, Elsevier or Clarivate Analytics already monitor things like dramatic increases in the number of articles published. It's why excessive self-citation can and has lead to journals getting delisted.
However you can still write to them to highlight potential problems. If you want to do this, the best way is to use their "contact us" forms on their website. Here's Scopus's page on it, and here's Web of Science's. Be prepared for the exchange to go like any other investigation - you may be asked to provide proof.
You should not rely on indices and metrics to judge the quality of a journal. Rely on the journal content and on colleagues who have experience with the journal's review practices. There is no reason to alert any index.
If your library is paying for the publication, you might suggest the librarian bring it up with the publisher's sales staff.