After wrestling with this for a few days it's time to report it/reach out to the community.
I have uploaded a set of jpgs to the default content library, which has the default security settings:
The security rule verification indicates that I do have read access. Worth noting that I have tried all the below both with myself as a regular user, and with all content admin, security admin and root admin rights given to my account. Same thing happens.
The files uploaded to the content library have rather generous rights, to rule out issues there I've set them up so anyone on the server can read those files.
After creating a new app, I can then browser the available images in the content library, and set the thumbnail:
Problem is that the thumbnail then does not show up on the app... Not while editing the app, and not after publishing.
I suspect it being some kind of right issues though, as doing the same thing on the server, while logged in as superuser, works.
I can then set app thumbnails and view them also when the app has been published - but only as long as I am accessing the app as superuser (i.e. the user used to install Sense). If I access the app using my own personal account, the thumbnail does not show.
This whole thing is a bit strange as I am using a pretty much vanilla, out-of-the-box setup of Sense v1.0.2.
On the other hand, if this was a general problem/bug, I would have expected more reports of it here in the forums...