Can a paper get rejected in the copyediting phase (after peer review acceptance)? A journal with high impact accepted my paper after peer review.  In the copy-editing phase I noticed some errors -- mostly mixed up references.  Can the paper now be rejected due to these errors?  What about if I want to update some references?
Formally, a paper can be rejected at any time, even after printing.  E.g. IEEE describes such cases, which are mostly plagiarism-related.  In your case of mixed-up references, a rejection is unlikely.

Updating references should be a non-issue in the early copyediting phase but problematic in the late stages.  You might have to live with published wrong references.