The fact that one of the pages is working correctly is promising - just means we have to track down what's different between that page and the rest.
First I would do a very careful check of the Vimeo privacy settings of both the videos themselves and the albums. With albums, you really just want to make sure that they're not password-protected (screenshot). With the videos, do a close review and comparison of the privacy settings between the working videos (acceptance speeches) and the non-working videos. With luck you'll find a mismatched setting.
Next, I would follow that with a careful review of your Vimeo All Access settings. I noticed that there's a slight difference between your working shortcode:
[tubepress vimeoApiAccessToken="97b7984......128e04" vimeoApiAccessTokenSecret="28c2e8f.......2e1c3ab" mode="vimeoAlbum" vimeoAlbumValue="2932178"]
and the non-working shortcode:
[tubepress mode="vimeoAlbum" vimeoAlbumValue="2932187"]
Notice that in the latter case, you're not explicitly specifying the Vimeo access token and secret. This shouldn't be a problem as TubePress will fall back to the settings at WP Admin > Settings > TubePress > Feed > Vimeo All Access, but it's something to double check.
If after all of this you are still stuck, please consider (if you are able and willing) providing either Brandon or myself with a login to your staging site. That would probably help us troubleshoot the issue further.
Thanks!