What's the purpose of people shouting "Hello" into the phone several times after they've clearly been disconnected?

You have to keep in mind that while movies often have the motivation to depict reality and a realistic story in a realistic way, they still are in many respects subject to a certain degree of explicitness upto hyperbole, as is the acting of the cast.

So in this viewpoint, the actor actually saying "Hello?" even though hearing the obvious "death-tone" is a way to clearly and expressively convey to everyone that the conversation ended abruptly and unexpectedly for the character, even if a real person would maybe just "deal with it". An actor can't just reserve each and every emotional reaction to his inner self as that would not be too compelling to watch in the majority of cases. Even if the acting in movies might generally be less hyperbolic than in theatres, it's still acting and relies to a large degree on conveying emotions in a less subtle and more expressive way. (It should be clear, though, that I'm overgeneralizing things a bit here, but so does the question. There might very well be cases where this technique isn't employed.)

An excellent, albeit probably rather extreme, example that comes to mind here is the finale of The Silence of the Lambs, where Clarice phones with Dr. Lecter and after he hangs up she repeatedly asks "Dr. Lecter?" although it's obvious for everyone that he hung up. But her desparate and apathic repetition of this question disregarding this fact makes her reaction all the more emotionally intense. Now the usual case of people asking "Hello?" after the phone hung up might be less emotionally intense, but it nevertheless follows the same principles. The character did not expect the conversation to end and this surprise has to be conveyed, for which this technique has simply established itself as an obvious way to go, even if it might start to get old or not reflect reality perfectly.

First of all: in real land lines you don't get the dial (continuous) tone after the call has been disconnected. Especially, if it was you who initiated the call the connection is usually maintained. Catija's comment is spot on - it's the tone that is the mistake, not the actor's shouts.