How do I let the user specify for which UDP ports a dissector should be used?

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The preferred way to do this is to register a so called dissector preference (pun intended ;)) with the dissection engine. This will automagically add your protocol to the list in the protocol tree in the preferences dialog, and allows your users to enter the ports your dissector should register on. When they do you first deregister from all old ports and register again to the new ports. This is a common theme, see section 2.6 in doc/README.dissector and useful convenience functions are provided for this, e.g. dissector_add_uint_with_preference() and dissector_add_for_decode_as_with_preference().

I created a dissector under the assumption that a given dissector is applied to every packet picked up by Wireshark.

Incorrect assumption. Link-layer dissectors are applied only if the packet's link-layer protocol type corresponds to the link-layer protocol for that dissector. All other dissectors are applied only if another dissector that sees the packet decides to hand the packet to the dissector in question.

In your case, with a protocol that runs atop UDP, a dissector is called only if the packet is a UDP packet and, for the source and destination port numbers in the UDP header, either:

1. the dissector has explicitly registered one (or both) of those port numbers in the "udp.port" dissector table;
2. the dissector is set up the way Jaap suggests, and the user configures it to be called for one of those port numbers;
3. the dissector is a UDP heuristic dissector, and the packet hasn't been handed to another dissector before it was handed to the heuristic dissector to see if it looks like one of its packets.

So, for your case, Jaap's suggest, 2), is the correct answer.