jQuery is dual-licensed under the MIT and GPL licenses - you can choose whichever you want. If you want your code to be closed source, you want the MIT license.

You do not have to do anything about that - you can safely use it without any further thought.

What you need to pay attention to, is that while you CAN bundle GPL'd code with closed source code, you cannot use or derive from GPL'd code, unless your code is under the GPL too.

Thus, as long as you stick to MIT/Apache/BSD/LGPL libraries, you're safe. You can bundle GPL'd programs with your system, but you can't use and extend those sources, unless you release those parts under the GPL too.