I installed WordPress on a couple of different hosting accounts that I have on hand to try and see where I should place the final result. On one of those accounts I was not able to update one of the plugins that was not up-to-date. I also could not download any themes.
Some forum discussions that I’d come across indicated that this issue was primarily suffered by users who were hosting their site on a Windows machine. This of course caused many helpful individuals to rail against Windows and recommend upgrading to a Unix hosting account without actually addressing the particular problem directly. The fact that this issue started with version 3.5 only didn’t detract from their suggestion.
I finally found a useful post that pointed out the true cause of the issue and a simple workaround. Version 3.5 changed the algorithm used to determine which directory to use for storing temp files as WordPress updates or download modules. To restore the old behavior without having to approach one’s hosting provider for configuration changes one need only add or update the following line in the wp-config.php file:
Voila! Everything works fine, even on my more restrictive hosting provider.