In order to help, we need details.  What browser are you using?  When you press enter on the file, does it play in the browser or open another program?  Is the file actually referred to as a podcast?  We don't know, at this point, if the file is being played as it is fully downloaded into the browser or a player or if it is a stream that only plays part of the file, overwrites what it has played as it plays move.

Can you give the address of the page where the file link is?

Gene

I discussed the file type briefly but my main point is that using the context menu will allow you to save files on some sites and not on others.  this is not related to the file type, it's how the site is constructed. 

We don't know, but my guess is that, in this case, Internet Explorer is being used and the file opens in Windows Media player, hence the question of how to save from there. 

In the context of other browsers, not the archaic Internet Explorer, the file is played in the browser when you press enter on the link.  If you are on a site where save target as or equivalent doesn't work, you need to know that you can use the command control s while the file is playing, and save it while in the browser in that way. 

Of course, that presupposes that you are dealing with an actual file that is playing from the site as a file, and not a stream.  The stream plays a little of a file and then refreshes the buffer in the browser or player but the entire file is never available.  Just a little bit ahead of where you are listening.  It can't be saved because it is a stream, not a file playing as a file from the web site.  Since this is called a podcast in the question, the odds are that it is an actual file being played from the web site, not a stream as I am using the word.

Gene