Decide whether DFA have useless states
In order to show decidability, you need to provide an algorithm that will always halt, and yields a yes / no answer.

The following algorithm will return if there is a useless state in a given DFA (and can return the useless state).

Given a DFA $A$, run a BFS from the initial state ($q_0$), and mark every node that is being visited.

When BFS terminate (and it will, because we're dealing with a deterministic finite automata), every state that wasn't visited during the scan is a useless state.