Good eye--that is a Mets helmet Callison has on.
Of the players in the photo, Johnny Edwards wore no. 6 with the Reds and is clearly the player on the far left of the photo. Walter Alston is no. 24 just to the right of Callison. Dick Groat is no. 24 in a Cardinals uniform to Callison's immediate left. Curt Flood is just behind Groat's right shoulder. Just behind Flood is another Cardinal, Ken Boyer, with somebody in street clothes to Boyer's left. Roberto Clemente is no. 21 in a Pirates uniform. Behind Clemente are Billy Williams, no. 26, and Ron Santo, both Cubs. Behind Santo is Casey Stengel.
In addition to the guy in street clothes that leaves the player in a jacket facing Callison (Juan Marichal?), the player just behind Groat (Willie Mays?), and the player to Groat's right (I'm guessing it is Bill Mazeroski since I believe only the Pirates and Reds wore sleeveless jerseys then-the Pirate all stars were Maz, Clemente and Stargell, and that guy looks too small to be Stargell).