A friend of mine went to court for unlawful detainer. The case was dismissed. Does that mean if he tries to get another place it may possibly show up.

The fact that someone filed the case is public record. Since it was dismissed there should be little problem, but the record is there depending on how much someone wants to dig. And in some states that is merely a computer search. For example in MO almost all civil and criminal cases can be searched and the results shown.