You get the power to telepathically transmit one message into the minds of every witch or wizard on Earth, simultaneously. They will all recieve the message at the same time without distinction (eg, if you transmit in 1992, everyone in Chamber-of-Secrets-era Hogwarts would hear it, but, say, Lily & James Potter wouldn't, as they're long dead). The message can be about anything, but it's limited to only be one sentence long. Only witches & wizards pick this up this transmission. What is it, and at what date/period/era/etc would you send it?
I would transmit "Peter Pettigrew is the one who betrayed Lily and James Potter and killed those muggles, and he's still alive, hiding as a rat." As for the date, I'd go with the day Sirius confronted Peter and Peter staged his own death.The way Sirius was convicted of something he didn't do always bothered me. If you have the means to force someone to tell the truth, why convict them without a trial?
I don't know if people would automatically believe the magical telepathic transmission, but it should at least get enough people listening so that someone would be forced to take another look at that case, and so that an innocent man would be saved from more than a decade in soul-sucking Azkaban.