Elsevier production team messed up my paper. What should I do?

You could try contacting the editor in chief of the journal to see if they could get the problem fixed. This worked for me when I had similar problems with a paper last year.

Based on your comments, the typesetting problems are not just about ugly formatting, but they actually change the meaning of the article (and significantly increase the chance that people will misread it).

This is not explained clearly in your question.

Did you explain it clearly to the journal manager?

He might think that you are a perfectionist who is being a PITA because you want everything to look perfect. If he does think so, he would still be wrong, but the main issue here is how to convince him to correct the problems immediately.

Do not say: "The typesetting is all wrong!", like you did here. Typesetting is not the first priority.

Instead communicate clearly that "The errors introduced during the proofreading change the meaning of the article. The changed statements in the proof are plainly incorrect, and do not match my manuscript."

If you don't get anywhere with the journal manager, then talk to the editor. Emphasize that this is not just about formatting, but the meaning of the paper has been corrupted.

Unfortunately, I have witnessed such problems myself: whoever typeset the formulas had about zero understanding of basic mathematics and mathematical typesetting. Not only did they break all math typesetting conventions, making the formulas hard to read, but they actually changed the meaning of the formulas.

Independently from whether you can get Elsevier to fix the problems that they introduced, my recommendation would be to take your own version of the paper (the one that you produced yourself, without the additional errors) and deposit that version to an open repository, e.g., arXiv. (Depending on the journal, it is probably possible to do this while respecting the copyright transfer agreement that you may have signed.) If you use arXiv, it's probably a good idea to fill in the DOI field (to keep the link with the Elsevier version), and indicate in the comments field, e.g., that the deposited version is free of publisher-introduced errors.

That way, if Elsevier doesn't fix the problems in their version, at least you can direct your readers to the arXiv version. And even if Elsevier fixes them, you get the added benefit that readers who are not subscribed to Elsevier journals can read and cite your work. :)