I'm sorry for the naive question, but I'm a bit clueless about free-software licensing.
Is there any problem with using GPL-licensed front-end software (jquery + plugins, for example) on a for-profit subscription-based web application that has a closed-source back-end, so long as you keep your changes to the plugins open?
Would such an RIA be considered one whole piece of software? By that, I mean would you need to extend the GPL license to all your code (PHP, for example)?
In general, the answer is probably no, you would not be in violation, but like everyone else here, if you can afford to have one, consult your lawyer.
Using GPL code in conjunction with closed source code is ok as long as you distribute the source to your modifications to the GPL code AND the modifications do not link against non-gpl code. PHP and Javascript don't really have the concept of "linking" in the "compiled against" sense, so that clause doesn't do much in this context.
In general, a good rule of thumb is to look at your modifications to the GPL code and say "if someone else wanted to use this code in it's entirety, could they readily do so with what I have provided them?" If the answer is yes, you're probably not in violation.
All that said, go read the license. It's very explicit, and too many people argue about its meaning without having read the document itself.
Yeah, this is why I don't like GPL as a license for JS, it's not wholly clear what constitutes ‘source’ and what constitutes ‘distribution’ in this context, which makes the usual intuitive assumptions of how GPL works potentially suspect. Is your whole web app an ‘aggregate’?
I doubt in practice the authors of any JS library would object to you including that script in your app, as long as you play fair by the intention of GPL and contribute any changes back under GPL. However, for compliance purposes it might be a good idea to contact the copyright holders and request clarification, or an additional release under a license more suited to web scripting.