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The best I can make out:
Top Row: Possibly John Carradine, Abbey Lane or Charo (both Cugat wives), the artist himself-Cugat, Liza Minelli, Phyllis Diller, possibly Ernest Borgnine, or, a restaurant bouncer?, the following the most confusing of all: possibly Eddie Fisher and his latest squeeze, or, as some have speculated, restaurant owner Melvyn's "agent" with his girlfriend, although why a restaurant owner would have an agent is confusing, and finally possibly Melvyn himself?
Row 2: David Niven, Tony Bennett, Buddy Hackett, Liberace, Charles Bronson, Jerry Lewis (some had guessed Clark Gable, but ears way too small and he was long deceased)
Row 3: John Wayne, Hugh Hefner, Katherine Hepburn, Danny Kaye, Jackie Gleason, Barbra Streisand
Row 4: Richard Burton, Elizabeth Taylor, Sonny and Cher, Sammy Davis Jr. (??), Alfred Hitchcock (via Hirschfeld), Anthony Quinn, Frank Sinatra
Bottom Row: Rex Harrison, Kirk Douglas, Red Skelton, Bob Hope, Bing Crosby, Lucille Ball, Danny Thomas and Groucho Marx (what, no Zeppo who lived in Palm Springs?)