I don't have the slightest clue about current distros, only some generic Linux/ Unix knowledge, but I would assume that this is a permissions problem or possible the relevant .conf file is not being reloaded after the update. In any case, you'd get much better advise on such stuff on any Linux forum. The Adobe world is, after all 97% Windows and Mac and very few peopel wil lhave anything to say about Linux, not even in the Flash player forum...
Moving this discussion to the Installing Flash Player forum.
Yes, there was a message in there about needing permission for file sharing. Furthermore, after seeing the successful completion of the download indicated by a check mark, no file or icon was presented to me on my laptop, to click on and start the execution (installation?) of the Adobe program.
The Adobe version of its 18.104.22.168 that I was trying to install was APT for Ubuntu 10.04+, via Firefox 11.0 (Mozilla Firefox for Ubuntu - Canonical 1.0). The OS is Ubuntu 12.04, 32 bit version.
Update: It was suggested to me on linuxforums.org to install "Ubuntu restricted extras" which contained the Adobe flash player update and some other useful applications. Seeing a reference to this same download in the Adobe flash player forum advising it could be downloaded from the Ubuntu software centre, I did so and Flash Player is now installed and working on my system. Thank you for the assistance.