A client of mine wishes to not have to sort images uploaded into a post gallery, but instead rely on its filename for sorting (e.g. "01_sample.jpg", "02_sample.jpg"). This would save a lot of time for the client, and I'm wondering if this is possible to achieve using WP 3.5+ and the recent changes to Add Media?
When you or the client add the gallery shortcode, you can add an "orderyby" option to specify the order of the images. Per the Codex page on the gallery shortcode:
[gallery ids="729,732,731,720" orderby="title"]
... will do what you're wanting.