Question: We have had issues with Mootools not being very backward compatible specifically in the area of drag and drop functionality. I was wondering if anyone has had any similar problems with jQuery not being backward compatible. We are starting to use it quite heavily and are thinking about upgrading to a newer version to start using several plugins that require it. Will we have any issues if we get rid of the older version?

Answer: 
jQuery seems to be nicely backward compatible. I have been using it for more than a couple of years now through several versions of the core and have not had issues when upgrading except a few minor ones with some plugins. I would say that the core seems to be fine but if you're using a lot of plugins you might run into some problems (but these are usually easy to fix, or the new core has that functionality built in anyway so you can just drop them).
jQuery is so serious about backwards compatibility that they produce a "backwards compatibility" plugin for each release: <http://docs.jquery.com/Release:jQuery_1.2#jQuery_1.1_Compatibility_Plugin>. It let people who don't need backwards compatibility save on page weight.