Factual error: When Peter is walking Alissa home, the traffic signal at the intersection they stop at goes from red to yellow to green. Not what US traffic signals do - they go straight from red to green.
Plot hole: After Peter Parker is framed and arrested for selling government secrets to foreign organizations, he escapes police custody and goes home to retrieve his Spider-Man costume that was simply hanging in his dark room. If he was arrested for selling government secrets then surely the police would have searched his home and found his costume (as well as equipment) in the process. Since the police car was visible in front of his house, it seems very strange that police didn't search his home.
Factual error: Despite being a paraplegic, when Smythe is about to be lowered into the vat of chemicals, his legs are pretty toned and muscular. The show implies that Smythe had been wheelchair-bound for a long time, so even if he had muscular legs prior to his paralysis, the muscles would have atrophied.
Factual error: When Spider-Man and Doc Ock are talking in the lab, at one point, a shot of Doc Ock's face shows Spider-Man reflected in each side of his sunglasses. However, Doc Ock's glasses have a singular lens, and the straight angle of Spider-Man's reflections suggest that the glasses are in no way curved, so Spider-Man should only be reflected in them once.
Factual error: When Morbius is comatose at the hospital after reverting to his human form following his battle with Spider-Man, he is still wearing his trenchcoat, pants, boots, etc. The hospital staff wouldn't leave him in his outfit, they would dress him in a hospital gown. On top of that, he isn't even hooked up to any monitors.
Factual error: When Kingpin has Robbie dangling from a helicopter, Spider-Man jumps onto the helicopter and tells Kingpin he promised to release Robbie, to which Kingpin replies sardonically with "And so I shall." Neither of these two should be able to hear each other over the helicopter rotors. Spider-Man doesn't possess super hearing and Kingpin is a normal human.
Continuity mistake: When Peter wakes up from Baron Mordo's illusion, he is wearing a monk's robe with sneakers and is barehanded. He removes the robe, revealing he was wearing his Spider-Man costume underneath, but his gloves and boots magically appear on his hands and feet as well. (00:09:45)
Continuity mistake: After Wolverine is knocked unconscious by the voltage of the cage that Beast is trapped in, Beast is able to keep Wolverine from falling into the vat of chemicals below the cage by gripping the fabric of Wolverine's costume. Once the fabric tears away, Beast is able to grab Wolverine by the hand. Once he loses grip, Wolverine is able to grab onto the cage itself. When Genevieve starts shooting the laser gun at the Hobgoblin, Beast is again shown to be holding Wolverine by the fabric of his costume. (00:08:30 - 00:12:05)
Continuity mistake: When Spider-Man is battling the X-Men, he shoots webs at all of them, which they remove. Later when Spider-Man is in Xavier's study with the X-Men, Gambit is shown removing a piece of webbing from his right arm, even though he had already removed it earlier. (00:02:15 - 00:04:30)
Plot hole: This series is in the same continuity as the other Marvel animated series from around the same time - X-Men, The Incredible Hulk, Iron Man, and Fantastic Four - by virtue of each aforementioned show crossing over with at least one of the others. This episode, which originally aired on October 17, 1997, establishes that Captain America had spent the last 50 years locked in another dimension with Red Skull, and the episode ends with he and Red Skull once again becoming trapped in the aforementioned dimension. However, the final episode of Fantastic Four, entitled "Doomsday," which originally aired on February 24, 1996, features a cameo by Captain America in the present day, attempting to stop a rampaging Dr. Doom.
Revealing mistake: The same shot of Beast looking dejected after Spider-Man calls him "blue boy" is used again a few minutes later when Wolverine is telling Spider-Man that he doesn't have to carry his burden by himself. (00:16:15 - 00:19:15)