How did the Ministry locate Muggles who have seen magic?

I'm using an example from Harry Potter and the Goblet of Fire for this question, however, this goes for any other event.

Meant a fair old bit of paperwork, I can tell you, what with the Muggles who spotted the body parts they'd left behind...

What if Muggles were to leave the scene of a magical encounter? How did the Ministry get to them to modify their brains? I understand that there is the situation in which some people wouldn't believe it, if the Muggle told stories, but still. Some people would believe, and tell other people.