Looking around, I found the following somewhat cryptic advice from hubi over on http://aptosid.com :
In about:config you should see helpers.global_mime_type_file which should be set to /etc/mime.types, and latter file should be available. And there should be a /etc/mime.types.
My installation passes this test, so the problem has to be somewhere else. I ran out of things to try, so I posted the following plea for help to the Debian User Forums :
Ran into a strange problem. I follow the "testing" distribution, so up until yesterday I was using Iceweasel 8.0 and now I have 9.0.1 installed.
At some point, the "Open" and "Open containing folder" options in the "Downloads" window stopped working. They used to work, I think, but now they do nothing. They are not "greyed out", yet choosing them elicits no reaction.
Based on a web search, I looked at "about:config", and confirmed that "helpers.global_mime_type_file" is set to "/etc/mime.types" - that file seems to be OK. I'm not sure about the /etc/mailcap file - the entry for "image/pdf" refers to the program "display", which is part of ImageMagick and does not (AFAIK) know how to display PDF files. Obviously, I would rather have it run "evince".
Also, I noticed that the file "/etc/mailcap" does not seem to belong to any package. Instead, there's a file "/usr/lib/mime/mailcap" which belongs to the "mime-support" package. On my system, that file contains nothing but comment lines.
I tried running "update-mime" but this has no effect on the problem.
I have both "nautilus" and "pcmanfm" installed. If Iceweasel would run either of these when I click on "Open containing folder", that would be fine, but it does nothing.
I ran "sudo grep iceweasel *" in /var/log, but saw nothing that would indicate that Iceweasel writes anything (like, say, an error message) to the log when I click on "Open" or "Open containing folder".
All replies greatly appreciated.
So, hopefully someone will reply.
You can look in ~/.xsession-errors if it gives any output (or open iceweasel from the terminal and look for the output when you click on those actions).