The main problem I have with all of the aforementioned examples of the clairvoyant murder mystery no matter that some of them are quite reasonable films is that they are murder mysteries first and foremost. In them, the clairvoyant is no more than a detective who follows a trail of clues by extrasensory means rather than standard ratiocination. What they are not are explorations of the life of a clairvoyant and what it is like to have these powers or even the origins of the powers, which is what you would expect a fantastical or science-fiction film to be about. They are essentially fantasy films that come with both of their feet standing in the mundane.
In this respect, Baffled! is no different. It plays out almost entirely as a murder mystery. Occasionally, Leonard Nimoy gets a few psychic flashes that have to be interpreted but this is no different than a standard detective finding a clue, while he and Susan Hampshire seem not unlike Miss Marple or Inspector Morse as they run around a country mansion trying to solve the puzzle. The mystery is not terribly interesting or that well written at one point, Nimoy and Susan Hampshire conclude that because poison was placed in Vera Miles orange juice, Signor Virelli (Christopher Benjamin) might be the likely killer on the grounds that Virelli is Italian and Mediaeval Italians used to poison their rivals wine. (These days this is something that would get called racial profiling). There is also an improbable denouement based on people wearing lifelike disguises.
Towards the end, the film throws in an occult conspiracy angle that is not particularly well explained. (Clearly, this was setting up a shadowy cabal for the presumed series to follow). This taps the occult and devil worship movie fad that was all the rage at the time after the success of Rosemarys Baby (1968). Baffled! was made just before The Exorcist (1973) came along and made a sensation out of the deviltry movie. The one interesting thing is how Baffled! prefigures the underlying attitudes towards youth that comes through in The Exorcist there is the sense that possession or coming under evil influence is something that causes a pubescent girl to suddenly start acting in adult ways. For The Exorcist, it was Linda Blair masturbating and mouthing obscenities; here, far more mildly, it is young Jewel Blanch putting on makeup and dressing up as an teenage girl looking like she is about to go out on a date.
The fascination Baffled! holds is that it features Leonard Nimoy who was just caught between his signature role of Mr Spock following the cancellation of Star Trek (1966-9) and the emergence of the Trek fan phenomenon. Here Nimoy is young and at the height of his sex appeal. His part as Tom Kovac is somewhat of a jolt to watch after being used to him as Spock we get to see him smiling and laughing for one, which is something you are not used to seeing Nimoy do. The character is even played as somewhat of a playboy not long after meeting her, he is happily hitting on Susan Hampshire and telling her Youre a great looking chick.
Film online in several parts beginning here:-