I know jquery have backwardscompatibility files.
But if you link to this specific version: http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js you don't need backwardscompatibility files. I want to know if http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js also is going to work with newer browserversions. Then I don't need to upgrade my jquery to newer versions with the risk that the website doesn't work well anymore.
I'm sure there won't be issues with newer browser against an older jquery version. Jquery itself is pure javascript - so I guess this shouldn't be a problem.
You'll probably getting into trouble when trying to implement newer features of you page that may require new jquery plugins...