We also use the same version that comes in Rhodes 5.0.2 for compatibility of the devices.
Do not try with more recent versions.
I don't use jqmobile-patch.js at all. It may be required for Windows Mobile - not sure, but there is some WM-specific code there. It also has support for "wait pages" which I see as an abomination that I never use.
1.4.x is much better performing, and has greatly simplified the complexity of listviews and buttons. On the other hand, it will take a great deal of work to change over an existing application, so I would recommend it only for new projects.
1.4.x has some strange ideas about page events! The new page container widget will drive you nuts. This is still settling-out, and I don't expect the page events to really make much sense until 1.5. Fortunately, extended support for the "deprecated" page events has been promised, so the old page events will not be removed until JQM 1.6.
The danger of *not* updating is that eventually JQM 1.3 will stop working with newer browsers. JQM only supports one version back, and I'm not even sure they are even doing that, as there was recently a 1.4.x release, but no corresponding maintenance release to 1.3.x. I would have expected one after the release of iOS8/iPhone6.
I think for many situations, it would be good to explore alternatives to JQM. It's not a good solution, for example, on under-powered or memory-limited devices.
Thank you for your comprehensive reply!
For new projects I will definitely update or explore alternatives to JQM.