It would be nice to be able to open a URL directly in jEdit, by pasting it into a text field. The UI change could be as simple as changing the label of the text field at the bottom of the File -> Open dialog text to something like "File name / URL:".
Of course, this would not do "the right thing" in the bizarre case when you have a directory structure like /foo/http:/example.org/, just happen to be in /foo, and enter the path to a file in http:/example.org/ with an extra slash after "http:". According to POSIX, it should simply ignore the extra slash, but it would probably be safe to assume that this is very much an exception. Alternatively, a switch of some sort could be added to handle URLs completely separately, or we could require the use of file:// if you really want to use such paths.