To anyone; to everybody — indicates that the action is directed at any person (no specific recipient).
このことは誰にも言わないでください。
Please don't tell this to anyone.
彼は誰にも優しく接する。
He treats everyone kindly.
そのプレゼントは誰にも喜ばれるだろう。
That present will probably please anyone.
By anyone; anyone (as agent) — used to indicate that an action can be done by anyone or that someone might do something (often in passive or potential constructions).
この問題は誰にも解ける。
Anyone can solve this problem.
このドアは簡単に誰にも開けられる。
This door can be opened easily by anyone.
その秘密は誰にも知られてはいけない。
That secret must not be known by anyone.
In everyone; within anyone — expresses that some quality or feeling exists in every person.
誰にも弱点がある。
Everyone has weaknesses.
誰にもやさしさの一面がある。
There is a side of kindness in everyone.
成功する可能性は誰にもある。
The possibility of success exists for anyone.