On the wall of Max's workshop is a framed poster of Randi - this is The Amazing Randi, a magician turned skeptic and debunker of fake psychics, who is obviously the model for the character of Max Dyson.
While the first episode of the new series that aired on ABC, this is the second episode in the Columbo series to feature the world of magicians, mentalists, and magic guillotines; the first being Columbo: Now You See Him (1976) TV. There is even a similar scene with Columbo in a magic shop being given a demonstration of a guillotine trick where his finger (in the original episode, the trick was large enough to include his whole hand) appears to be in danger of being cut off.
The psychic research foundation where the testing takes place is the Annemann Institute. This is an homage to Theodore "Theo" Annemann, a famous American magician from the first half of the 20th century. His specialty was Mentalism and he heavily influenced both mentalists and magicians who came after.