The Return of Hydro-Man: Part 1 - S5-E7
Stupidity: When Spider-Man is working in the lab, he uses his webbing to barricade the door shut so no-one interrupts him. When Debra Whitman shows up and asks who is in there, he identifies himself as Peter Parker. When he is finished with his work, he leaves out of the window so that by the time the security guards break the door down, he has vanished. Since he used his webbing to keep the door closed, it would be pretty easy for Debra and the security guards to figure out that Peter is Spider-Man since Spider-Man's webbing is at the scene and Peter seemingly vanished into thin air.
Sins of the Fathers Chapter 5: The Rocket Racer - S3-E5
Stupidity: The huge rover that the criminals use to aid in their bank robberies tears up the streets they travel down, which leaves a huge trail for the authorities to follow and track them down. Adding to the stupidity is the fact that the highly intelligent Spider-Man doesn't think to follow the path of destruction they leave behind to locate them.
Neogenic Nightmare Chapter 1: The Insidious Six - S2-E1
Stupidity: When the Kingpin is breaking all of the supervillains out of prison, Shocker, Scorpion and Mysterio all have their costumes, weapons and gadgets conveniently stored at the prison, which makes their escape easier. Surely a prison wouldn't keep superpowered weapons and costumes in the same place where the inmates are being held. They would be stored in a federal evidence locker.
Six Forgotten Warriors Chapter 4: The Six Fight Again - S5-E5
Stupidity: When the Kingpin has acquired all six keys required to access the doomsday device, he gives every member of the Insidous Six a key and promises them a share in the spoils, despite knowing that one of them is a traitor. He even acts dumbfounded when the Chameleon reveals himself to be the traitor moments later.