The race finish they show of Lucky Lady winning in Rio is actually the finish of the 1968 Melbourne Cup won by a horse called Rain Lover.
The circuit board that Barney puts into the computer has a "GE" logo on it. It does have a couple of transistors on it. This is an appliance part, most likely a control board from a GE oven or washing machine.
Possibly as an in-joke, one of the horses mentioned by the announcer at the beginning of the episode is named "Dirty Harry." The M: I episode "Run for the Money" was broadcast on December 11, 1971. The movie "Dirty Harry," starring Clint Eastwood, was released on December 23, 1971.
Every so often two different TV shows unintentionally intersect which in this case is Mission: Impossible and Mannix, which were both produced at the same time by Paramount. In the opening teaser, Trask goes into a business that is a front for an illegal gambling operation. When he leaves the store the car he's in drives by a rather small city park. This is the very same park that lies about a hundred yards down the street from where Mannix has his office and is often seen on that show.