After some recent set of upgrades I had the same issue on several wordpress sites. Going to an album page would show the list of galleries (with thumbnails and description). The issue is when you click on a thumbnail the gallery page opened has no thumbnails.
After disabling all the plugins on one site and turning each on I narrowed it down to the Jetpack plugin. Disabling the full Jetpack plugin is really not a solution for these sites. I narrowed down the issue to the Jetpack Publicize and Sharing parts. By clicking on Learn More on these two and deactivating.
Hopefully this will help someone out. Maybe someone on the Jetpack or NextGEN Gallery team can figure out the conflict.
Details for the sites:
NextGEN Gallery 1.9.10
Let me know if I can provide more information. Not marking this resolved since this is only a work around.