Maybe I've been staring at this too long and am missing something obvious. I do this duplicating of the live site onto the dev site often, but today it's broken.
I created a copy of our site. It's on Drupal 7 and CiviRM 4.7.22. I can log into the site and visit CiviCRM. When I try to register for an event, it fails with errors. I turned on all the error reporting. It shows it is failing because it is using the wrong database user - it's trying to use the database user for the live site instead of this dev one. Everything is correct in the settings file - it links to the right database user. So where else should I be looking to find a place where it is looking at the wrong database user? Thanks!
UPDATE: Well, I ran an update to 4.7.30 and now it's fixed.