Technically, the second half of a two-part crossover, with the initial episode ("Novel Connection") airing earlier in the week on Magnum, P.I.
Dorothy Loudon replaced Angela Lansbury as Mrs. Lovett in the original Broadway production of Sweeney Todd.
Render unto Caesar: even though they are in Hawaii, circa 44 minutes in, the fire dancing seen in the background is originally from Tahiti and not Hawaii. French Polynesian culture---mainly that of Tahiti---has been passed as Hawaiian by both Hollywood and the Hawaiians. The reason is two-fold: 1) Tahitian women (vahinés) dancing (tamure aka o'tea Tahiti) as well as men (tane) fire dancing is more visually appealing and therefore more exciting to film than the mild and subdued dance from Hawaii (hula). 2) When Hawaiians became aware of Tahitians' sexy dances, muslic and culture, they brought it to Hawaii. Routinely, Tahitian vahiné dancers are showcased in "Hawaiian" restaurants on the Hawaiian islands, without ever disclosing to tourists that they come from Tahiti. Therefore American (and European alike) tourists are erroneously led to believe that they're watching authentic Hawaiian dancing, when the hula (slow, rhythmic motion of hands and arms while turning to slow ukulele twangy guitar music) is very different from Tahitian tamure, which involves very swift shaking of the posterior, in a figure 8, to rapid fire Tahitian drums. The same, the men (tane's) fire dance is ominpresent at "Hawaiian luaus" across the 50th state.
The "Novel Connection" (S7, E8) episode of "Magnum, P.I." originally aired 11/19/1986, then continued on the "Magnum on Ice" (S3, E8) episode of "Murder, She Wrote," which originally aired 11/23/1986. Both episodes are available on the Season 3 DVD set and Complete Series set of "Murder, She Wrote," as well as the Season 7 DVD set and Complete Series set of "Magnum, P.I.".