Can't add media to post/page after upgrade to 3.8

Just did a test upgrade on a staging site to WP 3.8, and now when I add media, I’m getting issues — no errors displaying though, nothing in the error logs either. When I upload a new image, it displays in the add media window just fine, I click “Insert into post” and nothing is inserted. I try the same with existing media files, and the library is a blank page (when I go into the Media library directly, all images in the library appear with no problems, but from inside the Edit Post/Page screen, it’s blank.)

I’ve turned off all plugins, no change. Switched to default theme from the site’s custom theme, and presto, it works again. So the problem is almost certainly in the theme itself. However, without anything in the error logs, debugging this issue so I can continue using our custom theme will be most problematic.

Anyone else experience this issue with a custom theme? What do I need to add/edit to correct this bug?