The title doesn't make a lot of sense until you realize that the Riddler's question mark is a major icon of the movie. Bruce addresses that if he finds happiness with someone he may be willing to give up being Batman, so the title of the movie could more accurately be "Batman, Forever?" An interesting case of the absolute lack of a Title Drop.
The title drop happens in a deleted scene where Bruce finds his father's journal, discovers that it wasn't his fault his parents were murdered (they were going to the theater anyway) and him finding peace and going on with his mission, declaring to Alfred "I'm Batman... forever." Way to screw that up, WB.
There is a scene in the finished movie where Bruce relates to Chase how he fell into the Batcave as a small boy after running away from home on a dark and stormy night clutching his dead fathers journal (which admittedly loses relevance without the above scene) and remarks "I fell...forever". That is as close to a Title Drop as the movie gets, and basically what it means is Bruce thinks he is doomed to be Batman and is still falling through the metaphorical darkness. The central theme of the movie reflects this as Bruce is wondering if he can retire as Batman.
Another example can be seen when Dick Grayson (as Robin) announces that he is going to help Batman rescue Chase and says: "I can't promise you I won't kill Harvey." Up to this point, Dick had been referring to Harvey Dent exclusively as "Two-Face"... so the fact that he is willing to think of his would-be victim as a human being rather than a villainous monster indicates that he probably won't kill him after all.
Two-Face reflipping his coin in that fight scene. He's not reflipping it to get a different result. He's reflipping it everytime Bruce comes within range.
As mentioned above on this page, Forever makes Batman's killing-of-mooks in the Burton films, despite going against Batman lore, intentional actions of canon, so that when he gives Dick Grayson words on why murdering Two-Face will do more harm to him than good, he isn't just preaching, he's relating from his own experience.
There's an infamous sequence in which Two-Face tricks Batman into a car chase. Batman gets away from him (using, yes, the ability to drive up walls), and nothing in particular seems to happen. However, Two-Face's first appearance in this scene is disguised as a woman pushing a cart in front of the Batmobile. This seems trivial, but notice the parallelism between this sudden stop and the one in Batman Returns, this time for an actual old woman, in the midst of Batman being framed as a mad criminal. This echoing of that incident by Two-Face indicates that he was more than aware of it prior to being scarred. And, his whole character becomes much deeper. He's now out to rectify his mistake by letting a madman lose on Gotham, but once he gets scarred as result of Batman's failure, he can no longer be objective ("Emotion is always the enemy of true justice.") and must rely on the coin flip. In one, fell swoop, a subplot from one movie becomes more significant, an action scene from another actually has a point, and a character becomes more than a one-note joke. That's some intense fridge brilliance.
Fridge Logic: Why the hell does Gotham City have its own currency?
Did nobody notice Edward Nygma chatting rather amiably with Two-Face at the penthouse party?
This is Gotham City. When the madman crashes your party, it might be a good idea to talk to him and see that he's having a good time—some of them are just crazy/amiable enough that it might work.
How did Nygma make any money on the Box? Since he designed it while he was working at Wayne Enterprises, wouldn't WE have held the patent on the thing?
Lampshaded by the Novelization. Bruce's corporate lawyers advise him of this and tell him to take Nygma to court, but Bruce declines; he says it would look too much like "sour grapes." And, although this is implied and not stated outright, he wants to give Nygma enough rope to hang himself.
Edward's apartment and cubicle is adorned with bobbleheads and fortune teller machines of a guy that's dressed in a green suit with question marks all over it; He even takes the jacket and hat from the fortune teller machine when he meets up with Two-Face for the first time. Who is this guy?
This one comes from earlier script drafts, but was lost in the final cut. In those drafts, this pixie-like figure was called the "Guesser", and he probably served as the Gotham Globe's puzzles-page mascot (it's never stated what his function was). Apparently, he was popular enough that merchandise was made in his image, and his likeness licensed out for fortune-telling animatronics.
Who the Hell puts a deaf man in charge of guarding a bank vault?
He wasn't deaf. He had something to help his hearing, but he clearly wasn't deaf.
So it's completely normal for groups of kids to go trick-or-treating (without parental supervision) at Wayne Manor, even though it's on the outskirts of town?
Parents don't have to be hovering over their kids' shoulders the whole time they're trick-or-treating. I don't know about your neighborhood, but in mine the parents often stood well back from their kids.
In this tropers experience the presence of parents significantly hampers the feasibility of carrying out any nessecary tricks.
Not to mention this is Wayne Manor - justified or not, people would probably be more comfortable being there as the Wayne family were well known, well liked, and lacking in any sort of scandal. Given that this Bruce was also more aware of the need to be Bruce as well as Batman, he's probably also started to make efforts to avoid seeming like a complete idiot with no day job.