<p>I know next to nothing when it comes to the how and why of https connections.  Obviously, when I'm transmitting secure data like passwords or especially credit card information, https is a critical tool.  What do I need to know about it, though?  What are the most common mistakes you see developers making when they implement it in their projects?  Are there times when https is just a bad idea?  Thanks!</p>

Be sure that, when on an HTTPS page, all elements on the page come from an HTTPS address. This means that elements should have relative paths (e.g. "/images/banner.jpg") so that the protocol is inherited, or that you need to do a check on every page to find the protocol, and use that for all elements.
NB: This includes all outside resources (like Google Analytics javascript files)!
The only down-side I can think of is that it adds (nearly negligible) processing time for the browser and your server. I would suggest encrypting only the transfers that need to be.