Many states are now offering audio and in some states video files of oral arguments. For example, if you have a moot court problem that involves Massachusetts law you might want to check out the Suffolk Law School oral argument page. There are no live broadcasts scheduled until February 2nd so you will need to look in the archives to find a video file. These are high quality video files with good audio.
Although the Massachusetts arguments are a good learning tool under any circumstances, you might be able to find an argument potentially relevant to your own moot court problem by checking the Supreme Judicial Court's site for a relevant case, noting the docket number and then finding the argument for that case in the archive.
Tech note - You will need Windows Media Player but the Massachusetts application supports the Mac version.