His behavior is inappropriate but not threatening. He is not able to listen. It may be the only way he knows to interact with people or he may be bored - either is very unfortunate. Tell your children to watch where they step in the meantime. A few times of dog poo on their shoes and they'll pay more attention.
In any case, use or borrow a camcorder and film him. Make more than one film, entirely unedited, illustrating the different objectionable acts. In other words, catch him in the act. Make at least 2 copies of the films. You will want one in case anyone loses theirs as you will be giving the original to the police.
Then, check with an attorney and show the attorney the films. You can bring along your landlord who, it seems, is very cooperative and accommodating. Based on attorney advice, you can then file a police report.
You will have both film and landlord corroboration for your story. It should be easy to get a restraining order at that point. Once that's violated, further legal action (and hopefully treatment) can be obtained.
Good Luck!