Mistakes were made by zombies. The sentence makes sense and it is passive voice.
I made mistakes by zombies. This does not make sense and is therefore active voice.
In passive voice, the subject is what is acted upon by the verb. In active voice, the direct object is what receives the action. While some disdain the use of passive voice, especially in formal reports such as theses, passive voice is a good tool when desiring to keep a certain subject as the primary focus of the writing.
Passive voice is awesome; just consider the Second Amendment:
A well regulated Militia being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
Look at how it fares with your zombies-test:
"A well regulated Militia being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed by zombies."