You need to troubleshoot the third party add ons ...
Delete one at a time then try a PDF file.
I'd start with McAfee SiteAdvisor since it's a Safari add on.
Quote from the McAfee website: "With SiteAdvisor software installed, your browser will look a little different than before."'
Once it's uninstalled quit and relaunch Safari to test.
If that didn't help, uninstall Evernote Webclipper, quit and relanch Safari to test.
And so on until you find the culprit.
Active plug-ins should be visible in Safari - Help - Installed Plug-ins
Some pdf's - often interactive ones - do need an Adobe plug-in or application to use them, or they show a message similar to the one you saw. If you can download the pdf - Reader should open it... if you can't - enable the plug-in from Adobe's preferences, then restart any browsers.
Thank you, Carolyn Samit and andyBall_uk, for your prompt responses and suggestions.
Although I didn't follow your recommendations, they gave me some idea regarding what to do to resolve the issue.
The solution is actually very simple. I uninstalled my existing Adobe Reader (using CleanMyMac 2 but I believe moving the app to trash should do it as well), downloaded a fresh copy (version 11.0.04) and reinstalled it again. When the software was being installed, it asked whether I wanted to make Adobe Reader (AR) the default PDF reader. I indicated OK and allowed installation to proceed and finish.
After installation of AR, I reopened Safari and went to a website to click the link to the pdf form. And lo and behold, I was able to open/access/view the document! It worked with a second website.
So the lesson is when installing an upgrade remember to make Adobe Reader the default PDF reader.
I hope that this procedure can help others resolve their issue if they have a similar problem.
The default application for opening items selected in Finder - be they .pdf, .jpeg, .txt etc - doesn't affect what Safari does with them in the browser. PDF's are usually opened with 'WebKit built-in PDF' unless an Adobe or other pdf plug-in is active. Reinstalling AR presumably reinstated the plug-in.
I met the same problem and reinstallation of Adobe Reader didn't work. Finally I resolved the problem. It's related to the security setting of Adobe Reader in Safari. This link is very useful: http://helpx.adobe.com/acrobat/kb/blocked-plugin-alert-safari-7.html