Ivy doses several men with her pheromone dust and gets different results for each. This isn't inconsistent writing, Freeze describes it as 'heating a man's blood' so each man she affects is only as dazzled as a man would be if severely aroused and flirted with (Dick is young and inexperienced so falls completely, Freeze is married and devoted so shrugs it off completely, etc.).
This also explains why Bruce, who is shown to be in a long term but ultimately superficial relationship, is only slightly affected- he's not interested in sex or romance anymore as serious priorities.
Robin seems to be far more susceptible to Ivy's pheromones than Batman. Part of this may be because of Robin's natural bullheadedness, but a large part of it is that he always haphazardly breathes in her love dust, whereas Batman is always seen trying to shake it off.
Mr. Freeze is not having a moment of Bond Villain Stupidity at the beginning of the movie. His plan was to lure Batman (or even Robin) into a Friend-or-Idol Decision by freezing Robin and using that to cover his own retreat because his suit was running out of energy and his life would have been in danger if he had stuck around to fight Batman. In short, Mr. Freeze pulled a Batman Gambiton Batman!
The guy trying to save his wife saying "your emotions make you weak" definitely supports this theory.
The movie actually opens with a decent Visual Pun: outside the museum it lingers on a shot of a frieze before introducing Mr. Freeze. Too bad it's all downhill from there...
As Linkara pointed out in his review of the comic, the infamous "Bat Credit Card" actually makes a lot of sense when you stop to think about it.
Bruce Wayne is rich, and uses shell companies to funnel that money for crime fighting. It would be a lot harder to trace a corporate credit card than it would be to trace a card linked to an individual.
In other media, he's been shown needing to purchase things that he wouldn't normally carry on him (with the examples Linkara gave being diapers and coffee), meaning he'd need some way to pay for those items (and it would be too suspicious if he put it on a tab and paid it himself/had an employee of his pay it later).
He has a habit of customizing his crime-fighting arsenal around the bat motif - Batmobile, Batarangs, etc. It would be more jarring if he didn't extend this to something like a credit card.
Although he didn't mention it: A credit card is faster to use than a checknote even if Batman typed amounts on checks beforehand and let people keep the change, he'd still have to write who the check is to each time he paid for something with one - and that would also give his enemies a way of tracking him, and carrying one would be more practical than carrying around large amounts of cash in small bills. Plus, if the card gets stolen, he can merely cancel it, whereas he can't do anything about stolen bills, and it's a lot harder to stop a check.
Poison Ivy's constant changing appearance and various outfits aren't random, they represent the life cycle of a plant. When she first gains her powers her clothes are torn and she sprouts out of the ground like a new sapling, from then on her various costumes begin to make her more beautiful like a plant growing up and gaining strength. Her final outfit, which she wore when she seduced Robin in her lair, represent her full strength and most beautiful appearance, like a flower that has fully bloomed. Alternatively, the red color of her outfit could symbolize autumn, appropriate since she is at this point anticipating Freeze's apocalyptic winter. Her appearance in Arkham after her defeat is like a withered plant, representing how she is broken and how Freeze promises to make her life a "living hell".
One could also see her outfit changes as representative of the seasons. Her initial outfit is spring and represents her birth, literally sprouting from the earth full of newfound power and potential. Her green outfit represents summer and shows her at her best, manipulating and killing everyone she comes across. Her red outfit is fall, beautiful but signals the end of her reign. Then her final is winter with her ruined, broken and facing a literal freeze.
The song "Gotham City" describes Gotham as the city Batman hopes it would become and one he's fighting for.
The collection of bizarre themed gangs at the street race makes sense in terms of how crime has been evolving in Gotham throughout the previous three movies: As the mob from the first movie dissolved and supervillains with eccentric gimmicks began to become the norm and enjoyed brief but stylish and successful reigns of terror, it would stand to reason that the rest of the underworld was encouraged to follow suite in attempts to be the next top dog as flashy, high profile gangsters themselves.
Pretty much the entire rainforest ball in hindsight; Bruce's plan to use the Heart of Isis is marred by the fact that his plan means luring a dangerous criminal into a crowded event, a criminal who has been shown to have the stomach for killing, a very dangerous weapon, and a gang of violent henchmen, with only himself, Robin, and a handful of police officers between them to capture him. At best, a very poorly thought-out plan, and at worst, a plan where the Dark Knight himself intentionally endangered the lives of a ballroom full of people.
Not to mention Batman's stern "You have 11 minutes to thaw these people!" line he feeds to the overwhelmed Commissioner Gordon in the aftermath of the attack. This troper highly doubts that the GPD has any sort of portable, powerful heating devices to thaw the Gothamites out in time. Nice going, Bats.
Then again, considering this is Batman we're talking about, it's not a stretch to imagine he might've provided such devices for the GPD.
Also, while it's still not foolproof, their plan may have involved being more on guard and proactive in spotting Freeze before he gets inside, had Ivy not shown up and distracted them.