1. Why doesn't Vision go on the mission to Lagos?
When your team includes a vibranium/synthetic android with an Infinity Stone jammed in his forehead who can phase through walls and fly (and create capes), you would be kiiiinda foolhardy to NOT bring him on sensitive missions across the globe, since he could be pretty valuable. Especially when it involves a vengeful enemy intent on selling biochemical weapons to terrorists, maybe you should swap him in for Black Widow or Falcon.
Then again, maybe Vision was just way too busy at the Avengers compound reorganizing his sweaters (can we all give it up to whomever decided Vision should be wearing sweaters through most of the movie? Because that was seriously wonderful).
2. Why does Stark recruit Spider-Man?! HE HAS VISION!
Speaking of Vision - he pretty early on declares himself in favor of the Sokovia Accords and #TeamIronMan....and yet, when Tony realizes he's gonna need a whole squad to bring in Cap 'n Bucky ('n crew), he tracks down a teenager in Queens who's just SORTA powerful? Like, even if you DO know Peter Parker is secretly Spider-Man (they never really explain how Stark figured that one out), you realize that bringing a teenager to Germany for a superhero brawl miiiight not be the wisest move - especially when you have a damn GOD-LIKE ROBOT ON YOUR SQUAD ALREADY.
Note: alright - mayyybe you could argue that, at the time, Iron Man was pretty sure Vision would be busy guarding Wanda and keeping her on the premises of the Avengers compound. But the instant Wanda and Hawkeye escaped, Vision headed over to Iron Man's squad, and at that moment, he shoulda sent Peter back to Queens and away from the guaranteed-to-be-dangerous-as-hell airport fight. I mean - why is he risking an untested teenager's life?!
3. WHY DOES CAP KISS SHARON CARTER JESUS THAT'S CREEPY
Ya know, maybe it IS time Cap got a romantic interest who's under the age of 95, but did it HAVE to be his old flame's niece? It's creepy and bordering on incestuous - both of them have to realize that Cap's projecting his feelings for Peggy onto Sharon on some level, right? I mean, he JUST buried her and is clearly longing for what could have been.
Also, he does it RIGHT IN FRONT of his TRUE love: Bucky Barnes. Luckily, Bucky pretends to not be hurt by it.
That all being said, it's at least less creepy than in the comics, where Sharon was Peggy's little sister (although even that's been retconned so that Sharon's now her niece, but...c'mon, retcon it a little further away. Third cousins or something, at least).
4. Ant-Man's PRETTY blasé about becoming a wanted international criminal
Paul Rudd is utterly fantastic in the film - charming, funny, and the cause of at least two or three of the best moments in the entire movie. That all being said, WHY IS HE HERE?!
I guess what happened was...Hawkeye drove to San Francisco, told him that Falcon was calling in a favor, flew him to Germany, put him in a van, and drove him to the airport parking lot...all without ever telling him WHAT they actually needed him for? And when he DID arrive, Cap explains the situation AND that he would be a wanted criminal if he joined them. And Scott Lang's reaction is to basically shruggingly go along by saying:
"Yeah, well, what else is new?"
Uh, dude, you put your history as a wanted criminal behind you LESS THAN A YEAR AGO and JUST got back in the good graces of your (rightfully distrusting) ex-wife and your daughter, to whom you wanted to prove you were a hero and not a criminal. While you were doing the right thing by helpin' Cap, this was not a very wise move.
5. They build the most complex superprison of all-time and house...3 regular people with no superpowers (and one person who DOES have superpowers, who's being held in check by...a straight-jacket?!)
The Raft is introduced a little late in the film, and it's not even super-clear WHY they built this gigantic underwater prison - at the moment it's introduced, it's apparently empty. I guess they realized that the next time they capture a bad guy (such as the Winter Soldier), they better have a decent place to store them.
But who do they actually end up keeping in the most secure, most overprotected prison ever? Falcon (aka Sam Wilson, a guy with no powers), Hawkeye (aka Clint Barton, a guy with no powers), and Ant-Man (aka Scott Lang, a guy with no powers). Three of the people in this super-ultra-max prison are just totally normal dudes with no actual powers when separated from their wing-suits and Ant-suits (and, uh, bow and arrow set).
The only ACTUALLY superpowered person in the prison is Wanda Maximoff. And how do they tamp down on her insane, little-understood magical abilities? By...putting her in a straightjacket? That's it?!