with passive voice, the subject (if it is explicit) will always be set off in a prepositional phrase beginning with "by". so if it is possible to add the prepositional phrase to the predicate and have it make sense ("mistakes were made"..."by the man") then you have a passive.
for your example of changing a passive to an active, i would focus on the "by" prepositional phrase (ablative of agent to use a latin grammatical phrase). can the noun in the "by" prepositional phrase be used as the subject? does it make sense to "put it at the front of the sentence" (to put it basically).