The Australian and Germany release summaries mentioned above (they are the same) also included music unique to the prologue. This prologue has not been included on any North American DVD release of the film.
At the begining of the Australian Home video version (before the dedication to the Challenger crew), a prologue narrated by Kirk and containing scenes for the last two movies brings the viewer up to speed on what's happened. This wasn't included in the cinema release, instead the opening titles were slightly altered.
The film was originally released in 1986, which was the 75th Anniversary of Paramount Studios. Accordingly, the opening logo for the film originally had the 75th Anniversary sign on it, as did the original video release. All subsequent video releases (and at least some 35mm film prints) have included the regular Paramount logo.
The German theatrical version contains a short summary of the two previous movies, instead of the challenger-dedication. Later video versions had both the summary and the dedication.