Hmm... Have you made any customizations to the module? Are you using subclasses? The album dropdown is wrapped in the condition if($this->ImageGalleryPageID), so something is wrong with your ImageGalleryItem class not storing proper foreign keys.
No, no customisations. I had overrides in mysite for the two layout templates, but have moved them so they no longer affect the site. I'm using 2.3.2 and yesterday's SVN version.
I notice that my popup has the label 'image' down below the caption dialogue, while yours - on http://doc.silverstripe.com/doku.php?id=modules:image_gallery - has the label 'Album'. I presume this is where the dropdown should appear.
Naturally, I tried dragging and dropping images onto different Albums, but that didn't work. It's a slippery slope that Drag'n'drop: once you add it to one thing users expect it everywhere!
Check your ImageGalleryItem table and make sure they're all getting a ImageGalleryPageID.
They all have the ID 24.
Glad it's working. If you get a new UI working with ImageGallery, be sure to post your code so I can update the module to include it. Someone has already posted a way to get it to work with Galleria, so I'll be adding that in soon. Just be sure to undo any changes and update your SVN when I do add the change so you can continue to get updates without conflicts.
Galleria would be nice. I've had it kind of running on a static page, but it's a bit finicky - and the support forums were obliterated by spammers so not much help there. It is one of the nicest of the Jquery gallery displays that I've found so far.
Regarding writing a new UI: Can it be achieved as an override, or do you need to edit the PHP files?