Thank you for the kind words
In this particular case SCX248 was asked to change frequencies a number of times. In fact, at one point he was told to contact NY Approach on 132.4 and as you may have heard, that frequency wasn't even in use by NY Tracon yet. Fortunately that didn't cause any problems for the emergency aircraft; it was corrected fairly quickly. Imagine though if the situation was much more urgent and they were given a bad frequency...
Anyway, you have to listen to the recordings and whenever a flight is asked to contact another controller, you have to get that new frequency. This way you know what feed to go to in order to continue listening to that specific flight. Keep in mind though that Liveatc does not have feed coverage everywhere (yet) so it's possible you might not be able to hear everything. But in the case of SCX248, every frequency had a feed.
Another thing is each archived feed is divided into 30 minute segments and in this case the entire flight covered two of those half-hour segments.
And finally, the archives are stored in Zulu time so you have to convert the local time it happened into Zulu time to find the right archive. For example, if you want to find something that happened at 6:00AM local time in JFK, you'd have to add four hours to get Zulu time (6:00AM EDT = 10:00Z, 6:00PM EDT = 22:00Z).
I hope that helps...