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Gwen's death is a very effective Tear Jerker. Unfortunately, literally just before it happened, the movie has Gwen make a forceful speech to Peter about how she insists on helping him and putting herself in danger and he's not going to stop her. To remember this and that she was snatched up and murdered by the Green Goblin immediately afterward suddenly makes the whole thing seem like a badly-done black comedy.
The above scene is made worse by the fact that when Gwen falls to her death, the web Spider-Man throws to catch her takes the shape of a human hand.
Electro's first time in Ravencroft — he's tortured by a German scientist named Kafka who puts on classical music before the experiment. More subtle portrayals have existed in a 60s James Bond movie. If that sounds silly already, wait until you hear the dialogue.
When Max is getting turned into Electro, there's a big close-up of the electricity fixing the gap in his front teeth. What was the point of that?!
While the original trilogy had Uncle Ben appear posthumously and actually have a role in Peter's development, this movie does so with Denis Leary as George Stacy... just standing there and staring. Or sitting in a squad car... and staring. This is the source of the "always watching" meme.
The soundtrack chosen for the scene where a saddened Peter obsessively researches his dead parents. The contrast between the upbeat pop song and Peter's fixation and expressions is pretty stark.
Phillip Phillips: "I would do it for yooouuuu, for yoouuuu! Like a drum baby, don't stop beating!"
Harry Osborn's Wangsty behavior during his attempts to appear sympathetic ("Everybody wants my money!"), combined with the fact that he's sporting a haircut akin to that of Peter's infamous emo persona from Spider-Man 3, make him come off as overly dramatic for some.
Harry: AUGH! YOU'RE A FRAUD, SPIDER-MAN!!!
Note that he says that line in a Guttural Growler tone, adding another layer of narm to it. YOU'RE A FFFRRAAWWD, SPIDER-MAN!
Sure, you'd need a big dose of MST3K Mantra in order to take Spider-Man seriously, but any shot where a fully-costumed Spider-Man is sitting down and talking to Harry like a doctor telling his patient that he has cancer is one of the silliest visuals in the entire franchise.
Dane DeHaan's Harry, still sporting that emo haircut and backed by a melodramatic soundtrack, goes full ham again when he's trying to convince Electro to team up with him, and it is glorious. As an added bonus, there are some unintentional Ho Yay undertones to their conversation. However, it is also oddly tragic in a way.
Electro: Give me one reason why I should I trust you. Harry: Because I need you! Electro: You need me? Harry: Yes, I need you. You are my only chance that I have at surviving. Electro: You need me? Harry: Yes, I need you! I need you, please! PLEASE, I need you! PLEASE! I know what it's like to be thrown away! PLEASE, Max! I need you! I NEED YOU! I NEED YOU! I NEED YOU!
Taking Harry seriously as a Tragic Villain is also made much more difficult with how he acts like a stereotypical bad guy when he and Electro confront Donald Menken.
"Once you shut down the grid, Spider-Man will come for you, and I want you to make him BLEED!"
All of Times Square just staring at the Electro and Spider-Man fight like they're at a baseball game. This also happened in both Spider-Man 3 and Superman II, where the citizens just cheer for the heroes next to Ground Zero while the fight is taking place. It's clear that these citizens are just asking to be killed, and in other superhero films, you'd properly be seeing the citizens fleeing in terror rather than standing there and watching. It's even justified in Superman II somewhat by the majority of the battle taking place in the sky.
There are even a few people booing at Electro during the Times Square fight.
The cheering itself seems hilariously out of place. The danger surrounding these people is just too close for them to be standing around like they are. While it should be obvious that Electro is a real threat, none of the people are reacting like he's a real threat other than the police. Spider-Man himself doesn't even question Max's transformation or try to figure out his predicament. He just rolls with it like it's any other battle. Meanwhile, Gwen is holding onto a metal rail while all of this is going on. The sheer amount of dissonance in this scene is mind-boggling.
It's not until Electro tries to kill them all by trashing Times Square that the New Yorkers seem to realize getting too close to a fight between two superpowered people is a bad idea and start to panic and flee (still not Gwen, though).