On one of my web projects, I use a lot of javascript/jQuery code, which is pretty slow on browsers (Windows 7 x64), especially on IE.
I use 3 Ajax requests at the s
1) minify it
2) all the browsers come with built in debugging tools
3) reduce access to the dom by storing references in variables, don't look up the same element twice
4) separate and use a well known cdn
5) separate just cos its easier to manage
More jQuery tips here : jquery-performance-rules and here : improve-your-jquery-25-excellent-tips.
Make sure all your static resources are cached with no disk lookup
This library is pretty cool
Raw performance may not be your issue. If you notice poor performance on page load, see this article I wrote specifically about minimizing javascript execution on page initialization.
http://blog.lavoie.sl/2013/12/optimizing-page-loads-by-reducing-javascript.html
You can compare selector performance here: http://jsperf.com/
Just setup your HTML code, include jQuery lib and place each selector you want to compare as various test case.
Many of the jquery-performance-rules still apply,
Also have look at here jquery-proven-performance-tips-tricks
Since there are a lot of ways to improve code, especially with such big websites like yours, I think it will be more useful to just post the external links, since these are very nicely written and concise tutorials and tools. Here are some of them:
I would also recommend IDE for building web applications/websites called JetBrains' PHPStorm. It is commercial software, but definitely worth every cent, since it gives hints and tips for improvement while typing.