You really have to watch each episode two or three times in order to pick up on the subplots, subtext and foreshadowing that become important later.
The Symbiote seems to have two voices, one from the original person, and a second, much darker and more violent voice. The brilliance comes in when you realize it's the same actor as the person wearing it doing the voice each time, to represent that the Symbiote is bringing out the worst aspects of the person it's currently being worn by.
In the beginning of the show, why did Peter have a crush on Sally Avril? Because she bears a slight resemblance to the one he later comes to love the most: Gwen Stacy.
In the prom episode, Harry can be seen in the background applauding Mary Jane for winning Prom Queen. At the same time that the Green Goblin was battling Spider-Man. A nice little bit of foreshadowing.
In Rhino's debut episode, Spiderman points out his one weakness; that his suit is so well isolated it overheats with ease, and needs cooling down regularly; this is actually a problem real-life rhinos have, and they need to refresh/cool down themselves with water or fresh mud, or rest under a tree's shadow, when weather is too hot. Also, in subsequent episodes, Rhino rarely fights on day-time; he fights at night, or when weather is cool enough.
Possibly a coincidence, but Spider-Man's first fight with Doc Ock happened to be in episode number 8.
During its fight with the Sinister Six, why did the Symbiote only attempt to kill Dr. Octopus? Because The Doctor had threatened to "peel it away," subtly foreshadowing how clingy it really is to Peter.
Season 2's twist of Norman being the Green Goblin is set up remarkably well: in Season 1, during the scene where Chameleon is posing as him, and he hears that a thief has broken in, he asks, "A thief!? What did he steal?" putting emphasis on the "he". It's like he's implying that he's a different thief. And then, when the Goblin spots the faker, he pulls the briefest of double-takes. In addition, in the previous episode, the Green Goblin triggers Doctor Octavius's transformation by pulling out the safety key to engage the experiment. Norman Osborn then arrives and shuts off the experiment by inserting the same key. You know, the one the Green Goblin just stole.
Mary-Jane knows Peter is Spider-Man, much like the Parallel Lives story. Of all of Peter's friends, MJ is the only one who takes Peter's excuses at face value, she willingly stays back to save Peter the last dance as if she's expecting him to show up, she warns Peter about Eddie Brock's behaviour.
At first, Doctor Octopus telling Aunt May and Anna to step aside before he and the Sinister Six begin fighting Spider-Man in Group Therapy just seems part of his pragmatic, soft-spoken villainy - no more casualties than need be, especially someone he has no quarrel with. But then one remembers, in the comics, Otto was a huge Mama's Boy, and his mother frequently protected him from his abusive father. Otto probably has a soft spot for little old ladies that remind him of her.
Also a bit of a wink towards the original comics, where he tried to marry Aunt May.
There no way in heck Norman would've had the foresight to frame Harry for the limping leg thing, considering he just stumbled upon the passed-out form of his son after his bout with Spidey in the first season finale. Plus exactly what reason did he have to fake a limp in the first place?
Spider-Man had already accused the Goblin of being Norman. If Gobby had a limp and Norman didn't, it'd throw Spidey off that trail even if he didn't come across a convenient scapegoat.
I don't think crippling Harry was part of a plan. he does describe it as "serendipity"
Part fridge logic and maybe Fridge Horror; Rhinos suit. So, it covers his entire body in a metallic armour, to the point where the only exposed bit of skin is his face and he can only sweat through his face. How does he use the toilet?
He probably has some sort of tube for that.
The comics establish that he has a flap for that.
After curb-stomping Peter in their first battle, Venom declares his intent to attack everyone Peter cares about. His initial target is Aunt May. Peter arrives just in time and fights ferociously, even scoring a few good hits. Still, Venom could've definitely beaten him, but instead decides to reveal his identity as Eddie Brock and go after the person Peter loves the most - Gwen. This makes perfect sense: Eddie wasn't actually trying to kill May and was just toying with Peter, especially since he knew Peter would think of her as the first target. A few episodes earlier, he even says that he "still remembers what a great lady she is". Even if the symbiote was holding a grudge against May, which it has no reason to, Eddie wouldn't allow it to harm her. Might be a case of Even Evil has Standards.
Spidey using lockers to create a ringing sound that would disrupt Venom... yeah, try hitting a locker with a baseball bat. They don't work like bells, they'd get dented and make a loud, non-ringing sound for less than a second. Artistic License – Physics is pretty much the only way this could work.
It probably helps that Spidey has super strength and therefore hits much harder than a normal person.
It's not the strength that matters, it's the object that's being hit, specifically its shape and the material it's made of.