Japan’s intensely popular teen idol Goro Inagaki of the pop group SMAP may eventually prove a box office dream, but he’s proving a production nightmare on the remake of “Private Lessons.”Interruptions by fans and the press have shut down production three times since principal photography began two weeks ago. Fueling the frenzy, a trailer running in Tokyo theaters hypes the 19 -year-old actor, who also appears on three weekly TV shows on Japanese networks and one daily radio show. One source noted that his popularity has caused such havoc that press conferences are being held nearly every day on the set. The $ 3.5 million remake retains the same title and stars not only Inagaki but Joanna Pacula in the role played by Sylvia Kristel in the ’82 version. Seigi Izumi directs an updated version of Dan Greenburg’s original screenplay. As on the first film, Fred Chulack will edit with all post-production work being done in the States. Although it will be an English-language film there will be occasional Japanese exchanges. Warner Bros. has picked up distribution rights in Japan, but not the U.S. The remake is set for a spring 1993 release.