Did your client provide you with documentation of what dimensions are in use, what metrics.. what every page and every action should be tracking? Basically the be all and end all of what their site should be collecting?
Basically, you would take those documents an methodically test every page, every action, all critical flows through the sites to make sure that everything is tracking as expected.
Now, if this audit also includes reviewing that what is being track is what should be tracked, then you will also need to did into the admin, check all the settings, review all the attributions, and make recommendations on changes / improvements / additions to the tracking that should be considered.
If you received no documentation, then you really can't do much except for "ad hoc" testing... and if again, you are supposed to review what should be tracked, then you will have to use your best judgement to figure out what may or may not be broken vs what should be changed, added or removed....