Solomon Horowitz, the real-life father of Moe, Shemp, and Curly, appears as a street onlooker in the scene near the end where the Stooges crash their gurney into the car; he's the stocky man with moustache and glasses, wearing a fedora (he's also in the courtroom audience in "Disorder in the Court"). Solomon and his wife Jenny were in town visiting their famous sons when these classic films were made.
Ella McKenzie, the actress seen briefly as the desk nurse at the microphone, was not only the real-life daughter of Bob and Eva McKenzie (who, among other roles, played the Stooges' parents in 'The Yoke's on Me'), but was also wed to comic actor Billy Gilbert ('What you try to make for me--a fruit salad!?' in 'Pardon My Scotch") in 1937, the year 'Dizzy Doctors' was filmed.
The role of Dr. Bright is played by character actor Horace Murphy, who played Tex Ritter's comic sidekick in a number of low-budget Westerns, as well as other assorted roles. Check him out as Tom Murphy in MGM's "Boom Town" (1940) with Gable and Tracy (his scenes are at 28:38, 39:37, and 1:08:10). You can see Horace on You-Tube in the Tex Ritter Westerns "Rollin' Plains" (at around 4 mins) and "Trouble in Texas" (try 13:17 and 16:34). His last listed role was as a Farmer on TV's "Abbott and Costello Show" - the episode "Car Trouble" (watch on Hulu)-- Horace is on at 18:26. Same unmistakable face and voice ('Polish?! You idiots...that's MEDICINE!')