Bronson Pinchot originally turned down the role because he felt that it was too similar to his role in Beverly Hills Cop (1984). The producers did indeed want him because of his performance in that film. After a visit to Greece, Pinchot changed his mind and wanted to play the character inspired by the generosity of the Greek people.
The opening credits from Season 3 through the end of the series features a scene of Balki and Larry riding on a tour boat underneath a bridge spanning the Chicago River. The opening credits of its spin-off series Family Matters (1989) feature a scene of the Winslow family riding their bikes over the very same bridge from Seasons 1-3.
The producers originally developed the series to air in 1985. But Bronson Pinchot was already committed to Sara (1985). When that series was cancelled, the producers quickly hired Pinchot and continued developing their series to air in 1986.
The building used for the exterior shots of Larry and Balki's apartment for the first two seasons was the now non-existent Santa Rita Hotel, located at the south corner of S. Main St. and E. 11th St. in downtown Los Angeles, California. Since the series, the building has been remodeled and the upper stories removed. What remains of the building now houses several small shops and importers. Larry & Balki's second apartment as of March 2008: The apartment building seen in the exterior shots from seasons three through six is located at the northwest corner of West Dickens Avenue and North Clark Street in Lincoln Park, Chicago, and little has changed in appearance.
Balki Bartokamous is from the fictional island of Mypos. The island of Mypos is possibly based off the real-life Mediterranean island nation of Cyprus. Also interestingly enough, the name Mypos is derived from the Greek word for "maybe".
The play that they go to the opening credits is Neil Simons "The Odd Couple", which was adapted as a TV series, which aired on ABC, the same network as "Perfect Strangers", in fact at one point airing on Friday night where "Perfect Strangers" spent most of its run.