what sorts of evidence is permissible to prove adultery

Adultery generally needs a third party to substantiate the facts. Many times a private investigator is necessary. Regardless, under the new No Fault grounds law, if your ex- moves for a divorce based on No Fault and you are asking for a divorce based on Adultery, generally, the court will grant a No Fault divorce.  The importance of grounds may be relevant if there is going to be a custody dispute.