The final episode of ''M*A*S*H,'' which aired on CBS Monday night, may prove to be the highest-rated single episode of a series. Early overnight Nielson figures showed 72 percent of all New York City sets in use were tuned to ''M*A*S*H,'' reports Monitor TV critic Arthur Unger. The figure was 72 percent in Chicago and 82 percent in San Francisco. The current record is held by the ''Who Shot J. R.'' episode of ''Dallas,'' which captured a 76 percent share nationwide when it aired in 1980. The ''Dallas'' episode ran for one hour, however, while the ''M*A*S*H'' show aired for 2 1/2 hours. The high overnight figures represent the average viewership over the full length of the show. So, combined with the fact that the number of television households has grown since the ''Dallas'' episode, the extended length of the ''M*A*S*H'' sequence could turn out to be the most-watched (in actual numbers of people) program in sitcom history.