How to call latexmk in emacs, and jump to next-error

It's relatively easy to get AucTeX to run latexmk with C-c C-c. The following will add a Latexmk choice to the list of TeX commands:

(add-hook 'LaTeX-mode-hook (lambda ()
  (push 
    '("Latexmk" "latexmk -pdf %s" TeX-run-command nil t 
      :help "Run Latexmk on file")
    TeX-command-list)))

The trick is getting next-error to work. If you dig around in the AucTeX sources, you can probably find the regex it uses on TeX output buffers; it's not automatically applied to the buffer created by TeX-run-command. (You might also be able to convince compile mode to use this regex.)

Another approach is to redefine the variable LaTeX-command. This is a bit iffy because I think a lot of AucTeX functions assume they can tack command-line options onto this string and execute the result.

Adding %(mode) gives latexmk some more options like noninteractive if it is set so in auctex.

(add-hook 'LaTeX-mode-hook (lambda ()
  (push 
    '("Latexmk" "latexmk -pdf %(mode) %s" TeX-run-TeX nil t
      :help "Run Latexmk on file")
    TeX-command-list)))

Sorry I don't have the ability to comment, or I would just add this as a comment. Chris Conway's answer works, except that it should use TeX-run-TeX instead of TeX-run-command so that AucTeX knows to process the error messages.

(add-hook 'LaTeX-mode-hook (lambda ()
  (push 
    '("Latexmk" "latexmk -pdf %s" TeX-run-TeX nil t
      :help "Run Latexmk on file")
    TeX-command-list)))

It might also be wise to add something like

'("%(-PDF)"
  (lambda ()
    (if (and (not TeX-Omega-mode)
             (or TeX-PDF-mode TeX-DVI-via-PDFTeX))
        "-pdf" "")))

to TeX-expand-list and use "latexmk %(-PDF) %s" so that it will work in both pdf and dvi mode. Personally, I find it easier to use customize especially when you are experimenting.