Although Eddie Haskell's mother resurfaces a couple more times in the series, played by Anne Barton in those instances, this is the only time Ann Doran appears in the role. She does appear again in season 3 in Beaver the Magician (1959) as the mother of another one of Beaver's friends.
In this show and again later in the season, Karl Swenson appears as Eddie's father: Train Trip (1958). These are the only two instances where he appears in the series.
When Beaver goes to visit Eddie there is an Ohio State pennant clearly visible on Eddie's wall. This is an indication that Mayfield is likely in Ohio or at least the Midwest.