The court of public opinion does not require proof beyond a reasonable doubt. The court of public opinion makes its own evidentiary rules. In the court of public opinion we can consider hearsay, we can hear opinion evidence given by non-experts, we can accept leading questions, and can violate all kinds of other valuable rules of evidence. But all of us sitting in judgement in the court of public opinion should learn from the courts of law. They have some good ideas.
In the court of public opinion we should remember to listen to both sides. We should exclude dubious evidence. We should reject specious arguments. We should make our decisions based on the best evidence we can muster. We should not rely on second hand stories. We should be on guard against bias. We should keep an open mind. We should not base opinions on junk science. We should cross-examine those who testify to us (if we can). We should employ reason in weighing the evidence, rather than faith, emotion, feelings, or instincts. We should not guess or leap to conclusions. We should be diligent. We should do all these things (and more) if we are actually trying to discern the truth. We should try our best to be ideal observers.
Of course if we just want to mouth off none of this is necessary.