I’ve updated like 5 sites, 4 with appfinite themes, and 1 StudioPress, and I haven’t run into any issues whatsoever. The child themes don’t really have much to do with what was updated in WP 3.7. It’s hard to know what it is, since it could be just about anything. You may want to check with your host if they’re willing to help.
Thanks Eric. We did some sleuthing and realized that the issue is coming from NextGen Galleries. Unfortunately, this plugin has been sold to Photocrati and is now in conflict with every other plugin and theme known to man! Yikes. Anyhow, If anyone is using NextGen Gallery Plugin beyond the 1.9 version — do NOT upgrade to WordPress 3.7. Find an alternative gallery plugin or use the WordPress native media gallery BEFORE you upgrade. It will completely break your website regardless of the theme you are using. Just a “heads up” to people. 😉