"Undefined"

Maybe…
Are you using the wordpress 3.5?

No, it was in 3.4.2 and haven’t updated yet (our page is a web magazine, I have to schedule all bigger updates). Dunno, maybe the problem could be somewhere else too, any ideas to debug it?

Its application is running on windows or linux?

I have no idea, the host is bluehost. https://www.bluehost.com/ I guess it’s linux.

I don’t know this host…
Otherwise, you can try set the thumbnails directory with chmod 777 using your FTP client.

Good lucky!