As an example, consider the use of Tc-99m for diagnostic imaging in medicince:
Benefit: allows diagnosis of disease
relatively non-invasive
imaging allows better targetting in surgical interventions (eg. you can surgically remove a tumour with less exploration if you know exactly where it is)
Problem: radiation exposure for patient
Stray radiation exposure to others (doctors, nurses, relatives, ...)
production requires a nuclear reactor, which is expensive / a potential terrorist target / makes Greenpeace unhappy, ...
etc...