I am using the “attach” feature in the media library to link a set of images to specific pages. Our custom theme displays these attached images in a particular way. 
We are setting up WordPress as a CMS for a client and we don’t want them to have to attach images to posts / pages this way because it feels clunky to be editing page, then forcing the user to go to the media section and attach images to that page one by one.
I would really like our client to be able to attach a set of images to a post or page in a manner similar to the “featured image” feature. The user should also be able to add, remove and sort the images without leaving the page.
Actually, it’s very easy to attach images to posts and pages from directly within the editor. Just click on the Add an Image button (immediately to the right of Upload/Insert) to access the uploader.
You can upload as many images as you want to the media gallery for that page and edit the meta information attributed to each. Then click “Save Changes” at the bottom to save the images.
As far as WordPress is concerned, these images will be “attached” to the post or page on which you added them … no need to go to the Media Gallery to do an upload. They’ll only show up on the post or page if you click “Insert into Post” after you upload.
Update
For those of you who haven’t used this before … You can access the uploader through these icons:
The uploader itself will appear on the same page – you don’t have to go anywhere else to use the feature.
You can upload multiple images at once. Either click “Select Files” and select them one at a time, or select a bunch (click-and-drag) and they’ll all upload at the same time.
Once the images are uploaded, you can manage them inside the post or page’s internal gallery. You can re-tag images, change the details attributed to each, and drag them around to re-order things.
I hate to answer my own question, but I randomly stumbled across this WordPress plugin in a totally unrelated search today. It does exactly what I have been looking for.
http://wordpress.org/extend/plugins/attachments/
UPDATE
Turns out that this plugin doesn’t use the native attachment features in WordPress and creates a separate table that is plugin specific. For me that isn’t a problem, I just thought I would pass along the info.