The Dexter-Spider character looks similar to the title character from the 1958 movie, except, his head is a spider's head with many eyes, and he has many arms
Title card of the episode, "Don't Be a Hero" is spoofing the 60's Batman setting (as seen in the credits), except, instead of the Bat-logo, it is a D (for Dexter) with a no sign on it.
After getting bitten by the spider, everything goes trippy and you hear trippy noises that bears a striking resemblance to the Spider-Sense in the 70's series