Generally there is a difference between links in html formatted mails and links in plain text mails. While links in html mails have to be clicked only once, links in plain text mails have to be clicked twice. Further, when holding the mouse pointer over a html link, a tooltip is showing the url address of the link. A lot of html mails contain invalid links of the schema "#1437645". It seems to be internal html jumping marks, when opening such mails on the originator's website. And finally we experience html links, where the handing-over of the link from Pmail to the browser takes a long time (up to 10-15 seconds). I believe Pmail is checking the URLs in the background with different anti-spam or blacklist servers.

But the behaviour you described we cannot experience.

When I receive an email containing a link, it usually doesn't work.  Either nothing happens when I click on it, or the email contents disappear from the screen and a small triangle with an exclamation point appears in its place.  Many of the links that don't work seem to have the actual link contained in a file which I assume Pegasus has put on my hard drive.  But there are others that have the actual link right in the email.

 This is very frustrating and inconvenient.  Does anyone have any ideas?

Thanks. 

Tools > Options > Incoming Mail > Hyperlinks 

Make sure this is correctly configured.