The dolphin is an obscure reference to DUSO The Dolphin, a teaching aid from the 1980s.
Despite being a prominent in advertising for the series and a recurring element of the show and it's intro, the dolphin puppet is not prominently featured in the actual series.
- In "Mole Hunt," Archer is seen beating Pam with the puppet after a failed HR mediation.
- In "Mole Hunt," Pam uses it to explain to Krieger the importance of not raping the food in the break room.
- In "Dial M for Mother," Pam uses it to try to tempt Brett into having sex with her.
- In "Stage Two," there is a flashback of Archer beating Pam with the puppet.