Michael Forest reprises his role as Apollo from Who Mourns for Adonais? (1967) . Although the story takes place only a few years after the first encounter with Apollo, almost fifty years has passed in reality - the age difference is explained by having Apollo's life energy being drained by the The Realm.
The hologaphic cowboy on the holodeck is the character "Paladin" from the 1957 television series Have Gun - Will Travel (1957), a series which Star Trek series creator Gene Roddenberry had written 24 episodes for prior to Star Trek.
The scene in Recreation Room 6 is very reminiscent of the rec room scene in the TOS epidode "Charlie X" where Uhura is singing "Oh, On the Starship Enterprise" and Spock is playing the Vulcan lute. When Apollo starts singing, in the background you can hear a stringed instrument that sounds very simular to Spock's lute.
The aztec sculpture (by Special effects sculptor Dale Morton) in Kirk's quarters appears to be a copy of the one seen in the TOS episode "The Conscience of the King".
Most fans of Star Trek TNG will recognize the voice of the ships computer on Star Trek Continues as the voice of "Marina Sirtis" known as (Counselor Commander Deanna Troi).