It turned out Picasa has an extra privacy parameter on location data of photos that are going to be shared as public.
The "Show photo locations to viewers of this album" parameter must be checked for geotags to be sent with the photos metadata, even if those photos are already publicly shared.
See also OP's answer below.
Unfortunately it looks like your photos miss geographic coordinates data (no geotag).
In Picasaweb, open your photo and then click on the "full details page" link on the far right menu (for left-to-right languages). There should be
Longitude data. Like for example in photos from Bjørn's album (author of Leaflet.photo plugin): https://picasaweb.google.com/lh/photo/nfgH9Rj2jbZlllxLLM0aDNMTjNZETYmyPJy0liipFm0?full-exif=true
You can also inspect the JSONP response by simply typing your URL (
https://picasaweb.google.com/data/feed/api/user/MY-USER-ID/albumid/MY-ALBUM-ID?alt=json-in-script) in the browser location bar: you need
['georss$where']['gml$Point']['gml$pos']['$t'] attributes available for the plugin to be able to determine the location of your photos.