Question: I'm new to jedit, and I haven't yet found out how to open a new window. For example, I want to be editing one set of files in one space on my Mac, and edit a different set of files in another. Does anyone know how to open a new instance/window of jedit to make this possible?

Thanks

Answer: 
It's a new feature to 4.3. It's under View | Buffer Sets. You click on either the "View Scope" or "EditPane Scope" buffer sets checkbox. 

When you open a new View, it's a separate window instance. It has a buffer set and an edit pane. With more than one View open, you can decide to share buffer sets (global scope) or each keep their own (View scope). When you split the View, you add another Edit pane. Each can use the View's buffer set, or have their own (EditPane scope)

Global scope: All Views and EditPanes share a common buffer set  

View Scope: EditPanes in the same view share the same buffer set  

EditPane Scope: Each EditPane can have it's own independent buffer set.

The editpane scope works when you have split the view (view | splitting). You can look at files side-by-side, and each side can have their own buffer set. Very useful in comparing files in two different directories (one set per side), for example.
I wish there was an answer for this, since I'm constantly trying to open new instances of JEdit (despite being a daily user for several years now). But, as far as I can tell, you can't.

I have to assume this is another example of a good project getting over-architected.

Instead of allowing separate instances which logically associate different buffer behaviors using the built-in OS mnemonics, the JEdit crew have decided to create their own UI concepts. What OS lacks the concept of software instances and a task bar? Was it necessary to force a single-instance mode, and then re-create basic OS UI functionality in an obscure manner?

A hint for budding developers out there: if you're creating new terminology to handle UI concepts in your application, you're probably doing it wrong.