We study sensor minimization problems in the context of fault diagnosis. Fault diagnosis consists of synthesizing a diagnoser that observes a given plant and identifies faults in the plant as soon as possible after their occurrence. Existing literature on this problem has considered the case of static observers, where the set of observable events does not change during execution of the system. In this paper, we consider static as well as dynamic observers, where the observer can switch sensors on or off, thus dynamically changing the set of events it wishes to observe.