can jquery be a problem for large scale sites in relation to something like facebook, where a huge number of visits hit the site or the site containing a great amount of content?
why would it be a problem? JQuery is just an abstraction of JavaScript. High Scalability issues happen on the server side or are bandwidth related. Once a client has cached jquery (or heck it can be served by google) there should be no issues.
The cost of any JS library (jQuery or otherwise) is the additional bandwidth cost -- the big JS libraries having varying degrees of customisability but you will still tend to end up sending a lot of code that is unnecessary.
The real cost is client side computation cpst, but realistically anything you use a library for is likely to be something you would have to do anyway so i doubt there's to much additional load in that regard.
Jquery is a client-side technology written in javascript.
It can be a problem in terms of bandwidth required to serve the js files, or can be a problem if it makes lots of AJAX calls that create server load.
If you're worried about the bandwidth of the JQuery file itself, you can use Google's CDN to load JQuery. However, your website still needs to handle any actual XHR requests.
Whilst heavy use of jquery - or any other javascript library, for that matter - can result in a lot of AJAX calls to the server, the important thing to remember is that those calls are usually made to update some part of the screen. Not using AJAX would mean that the whole page would need to be refreshed, and this can often result in much more traffic to the server.
As usual, the actual bandwidth requirements will depend entirely on your application but, generally, judicious use of AJAX can improve the (apparent) responsiveness to the user, promote re-use within your code and make the structure of your application much cleaner.
jquery has the added advantage of making your client side code much more concise, easier to understand, and much more likely to be cross-browser compliant.
As other people note, there really there is no problem with using jquery/JS frameworks...
A rarity nowadays but what if Javascript is not enabled... its something you should be aware of, in that you should still enable users to access essential functionality without JS enabled.
Another factor to consider is that if you have heavy use of javascript, you need to be aware that a user's machine may not be high specced and they may be running many other apps &/or browser tabs.
This may translate into the user becoming unhappy with the experience on your site and is probably a factor in designing a site where you want a high market penetration. A peeve of mine, is I really dislike using sites that slow my browser down to a crawl and use a large amount of cpu and it seems to be something that is occuring more frequently.
So really there is no problem with using jquery et al, you just have to weigh up the pro's & con's which may or may not apply dependent upon your target audience.
As others have pointed out jQuery is a general purpose JavaScript library and hence you're bound to have your users download something that they're not using. Though mostly that won't be a problem in real life situations.
What I would rather worry about is to build large (complex) websites in jQuery since you're then effectively (unless you go completely out of your way) moving large portions of your business logic into JavaScript which will make your application far more difficult to maintain. And also far more complex to create.
According to http://docs.jquery.com/Sites_Using_jQuery big sites like Amazon.com, Match.com and Slashdot are using JQuery.