What are the problems associated with using JavaScript, and are there JavaScript techniques that you discourage?

Browser version incompatibility is the biggest problem. It requires knowing how each scriptable browser version implements its object model. You see, the incompatibility rarely has to do with the core JavaScript language (although there have been improvements to the language over time); the bulk of incompatibility issues have to do with the object models that each browser version implements. For example, scripters who started out with Navigator 3 implemented the image rollover because it looked cool. But they were dismayed to find out that the image object wasn't scriptable in Internet Explorer 3 or Navigator 2. While there are easy workarounds to make this feature work on newer browsers without disturbing older ones, it was a painful learning experience for many.
The second biggest can of worms is scripting connections between multiple windows. A lot of scripters like to have little windows pop up with navigation bars or some such gizmos. But the object models, especially in the older browser versions, don't make it easy to work with these windows the minute you put a user in front of them--users who can manually close windows or change their stacking order. More recently, a glitch in some uninstall routines for Windows 95 applications can disturb vital parts of the system Registry that Internet Explorer 4 requires for managing multiple windows. A scripter can't work around this problem, because it's not possible to detect the problem in a user's machine. I tend to avoid multiple windows that interact with each other. I think a lot of inexperienced Web surfers can also get confused by them.