What are the browser related issues for jQuery?

In IE8 most of the times Ajax calls are not working, its getting failed. The work around for this issue is you just add the moonscript reference in that page, it works fine.

First issue if client disable javascript. Browser compatibility Not secure

Javascript compatibility between Firefox, Internet Explorer and other browsers can make Ajax and Javascript effects a headache. Each browser does things just a bit differently, forcing Web developers to check which browser the user has and branch their code into if-else statements accordingly. Learn how to use the Javascript library jQuery to solve browser compatibility problems for you. Anybody who's ever had to code JavaScript for public access sites knows what a headache it can be to make that scripting language behave as needed in IE, Firefox, Opera, Safari and Chrome. I'm sure others have wished, as I have, for a one-script-fits-all form of JavaScript that would cure the browser compatibility headache once and for all. I can't yet say that jQuery is a universal panacea for this particular problem, but I can say...

Browser compatibility of jQuery plugin is an issue and needs lot of time to fix it.