What should I do if I found a citation error in a published paper?
Small errors that do not affect the results or conclusions of the paper are normally handled through publication of a correction (or erratum). This is handled by the journal editor, who will be in contact with the authors for confirmation that they agree as to it being an error, and provide for the exact correction to be published.
The journal that published paper should have a policy on corrections, check it out! Physical Review Letters’s editorial policies and practices state, for example:

Errata.— The Errata section contains notices regarding errors or omissions in papers previously published. Besides the standard Erratum, several special categories of documents may appear in this section. In the online journal, each of these documents involve bidirectional links between the original article and the document in the Errata section. The category of the corrective document is indicated in its title and in the link from the original article.
The standard Erratum is a statement by the authors of the original paper that briefly describes the correction(s) and, where appropriate, any effects on the conclusions of the paper.

Thus, what you should do is:

Make double sure it is actually an error.

Then ask someone else to double check it again. Preferably someone more senior, i.e. with some experience of academic publication.

Write to the corresponding author, pointing out the error. Be nice, and make real sure not to assume to worst.
You say “this is a pretty big mistake and suggests they haven't actually read the paper they referenced”: depending on context, it could actually be something minor like a copy-paste mistake (pasting the wrong reference, when they meant another paper)

If you do not obtain a response, or they respond but don't intend to correct the error, then consider contacting the editor.


I can understand why, as an undergrad, you would consider contacting the editor directly without writing to the authors first. However, as long as you remain professional in your correspondence with them, I think it's best to contact the authors first. It's more polite, and they may actually be able to provide you with some explanation you haven't thought of. Contacting the editor before the authors is somewhat overdoing it…