There is plenty of bonus material and foreshadowing about Borden's big secret that he's actually a pair of twins:
Christian Bale's performance is slightly different when playing the two brothers.
At the beginning Cutter tells Borden, "On some days you just don't get it do you?" One of the brothers, the one who wants to tie the Langford Double, is clearly the one who "doesn't get it" in the eyes of Cutter.
Borden says that he's "asked himself" many times which knot he tied on Angier's wife. He's talking about arguing with his brother. He also says he does not know which knot was tied, because that brother was not the one who tied the knot.
When Sarah says that some days Borden loves her and some days he does not. Borden explains in the end that only one of the brothers loved her, so when he doesn't mean it, those are the days when the unloving brother is playing Borden.
Angier notes that Borden's journal entry regarding what knot he tied had Borden "struggling with himself" and alternating between two different perspectives, which indicates that both brothers contributed their perspectives to the journal.
Borden uses his double trick on Sarah by breaking in to her apartment during their date and then magically appearing inside as she goes through the door. Borden's line of asking to be let inside for tea and then appearing with a tea kettle show that even this line was pre-planned.
Obviously, Fallon's sudden appearance and deep involvement in Borden's life, to the point of comforting his daughter, is because Fallon is also Borden.
When Sarah tells Borden that she's pregnant, he immediately says that Fallon should have been there to hear the news. In the same scene, Sarah notes that Borden doesn't love her today, because the brother playing Fallon is the one who loves her and is the father.
When Borden's daughter admonishes him that he promised to take her to the zoo, he's surprised and asks, "Did I?" then agrees to take her. He doesn't remember because he's not the brother who promised, but has to abide by the other Borden's promises. He then has Fallon take her, who is in reality the brother who made the promise in the first place.
Some of Borden's lines sound on the first view like he's speaking out loud to himself, but he's actually addressing his brother.
Borden asks Fallon for help in reminding Sarah that he (Borden) really does love her. This sounds like Borden is asking Fallon to be his wing-man, but it's actually the brother who is married to Sarah requesting that the other brother, the one who doesn't love her, to play his role as Borden more convincingly where Sarah is concerned.
When it all starts to fall apart and Sarah is being tired of lies, Alfred answers that lies are his life, before correcting it and saying lies are their lives. He's not talking about him and Sarah, but about both brothers.
Just before Borden is executed, he says, "Abracadabra." He's about to pull off his final trick: dying and still being alive.
The whole plot of the movie was based on the very same trick at the center of the plot, only not on stage. It was done with twins after all.
Borden assures his wife that after performing the bullet catch trick, he will return to her no matter what. Even if the brother performing the trick died, there would still be the one playing Fallon that day to return to her.
Olivia always addresses Borden as "Freddie," while Sarah always addresses Borden as "Alfred". Freddie is the brother that is in love with Olivia, while Alfred is the brother in love with Sarah.
Cutter insists that Borden must be using a double for his trick, but Olivia insists that she can see the bandaged stumps on his left hand both when Borden disappears and when he reappears, even though Borden wears padded gloves to hide his short fingers. As we later learn, the twin brother had willingly amputated his own fingers to match Borden's and preserve the kayfabe.
When Olivia begins working for Borden as a spy for Angier, she comes to believe Borden's trick is accomplished using a double, because she sees makeup, glasses, and wigs lying around. Angier thinks that these are plants by Borden as misdirection for her. Olivia's theory was accurate, but not in the way she expected: those items are for the brother who is posing as Fallon.
Alfred Borden, Robert Angier. Cutter, Alley, Danton, Alfred Borden, Robert Angier. (Because there are two of each.) Put 'em together, and what do you get...? ABRA CADABRA
The motif of "simple" tricks with Borden, whose own greatest trick is actually very simple.
Borden shows Sarah the trick behind the bullet catch, and is a bit annoyed when she immediately says that the simpleness of the trick is disappointing.
He tells Sarah's nephew not to tell anyone the secret of a trick, because learning the trick won't impress anyone.
Borden and Angier note that Chung Ling Soo's great trick is very simple, but requires him to "live" his trick to pull it off. Borden's simple trick is the exact same way.
The above motif highlights the Technician Versus Performer trope that divides the twin brothers. Borden is the Technician who believes that the trick's style is the most important part of it, while Fallon is the Performer who considers the effort and trouble put into the trick more valuable. This reflects in Borden being sent for execution and wishing he hadn't obsessed so much, while Fallon considers that Angier did terrible things, for nothing (for an illusion, which is nothing).
The motif of doubles:
The dove trick, in which one dove dies while another takes its place, mirror's Angier's version of the Transported Man. Borden addresses one as "the lucky one today." When Angier is performing his own trick, he'll have no idea which version of himself survives.
When watching the same dove trick, Sarah's nephew calls one bird the "brother" of the other. Borden's version of the Transported Man trick involves identical twin brothers acting as doubles of each other.
Cutter assures Angier that the only way he can think of to perform the Transported Man is with a double. Borden is using a double.
Angier's first version of the Transported Man involves him getting an imperfect double, which causes the trick to ultimately break down.
Tesla's machine creates doubles. When Angier asks which hat is his, Tesla responds, "They're all your hat." Thus, when Angier copies himself, both versions are him.
The three act structure of magic (the pledge, the turn, and the prestige) also outlines the shifting genre of the film. In the opening the story is framed as a realistic melodrama about two rivals trying to outdo each other (the pledge). Then in the second Tesla is introduced and his machine is compared to real magic and an element of fantasy is introduced to the story (the turn). Finally the nature of both Angier and Borden's tricks are revealed (the prestige).
Angier/Caldlow saying that he has always been Caldlow takes on an alternate meaning when you realise that he is a clone who had been created seconds before Robert Angier publicly died and therefore has only ever been seen as Caldlow and never Angier.
It's mentioned early on that Angier changed his name to avoid disgracing his family. Angier is a false identity adopted by Caldlow the same way Fallon is a false identity adopted by Borden
Angier's insistence that the Transported Man trick is more complex than a simple body double is not only due to how identical the Borden that emerges from the box is to the one that goes in the other box, but the fact that Cutter demonstrated a way to pull off the disappearing/reappearing bird trick (essentially a smaller version of the Transported Man that normally uses two identical birds) with only one bird, using a spring loaded mechanism to drag the bird out of the cage before it is crushed. Angier most likely assumed (at least initially) that Borden was using a larger version of the mechanism to move himself between the boxes.
There are parallels between Julia and the many clones of Angier who die by drowning (Angier felt guilty and wanted to experience what Julia had experienced in her last moments) and Sarah and Frederick Borden who die by hanging (this twin was indirectly responsible for causing Sarah's suicide).
Cutter insisting the trick can only be done by a Body Double is him understanding that Stating the Simple Solution is an Occam's Razor element. Angier wants there to be a grandiose and ridiculous reason for the trick because it justifies his hated rivalry versus something very easy that almost anyone could guess (even if The Reveal is impressive). Cutter as the most experienced magician among them knows that stage magic is never as impressive once explained as the reality.
In a fashion reminiscent of Quantum Suicide, each time Angier uses Tesla's device, a perfect copy of himself is executed. From the dying clone's perspective, he's the Angier who set up the trap and survived all of the traps except this one, while the one who survives remembers surviving every single trap. Angier has no idea and no way of knowing whether the consciousness that pulls the lever is getting executed or surviving each performance.
However the machine works, the original Angier is long dead by the time of the final confrontation between Borden and Angier. Either he was shot by the clone the first time, or he shot the clone and drowned himself onstage. The Angier killed by Borden is a man who Borden only met once before, never feuded with until then, and who is acting on nothing but a dead man's madness.
This means the original Angier never got to experience the crowd's admiration for doing this trick. He either got shot or was likely drowned in the demonstration for the theater owner.
Angier chose to drown his clones (rather than bury them alive or behead them or whatever) because Cutter had told him that drowning was peaceful and painless (Cutter probably made this up on the spot when he related the story at Julia's funeral in an attempt to make Angier feel a little better; that is, "She didn't suffer."). When Cutter tells him the truth, Angier gets an even sicker look on his face when he realizes that he's inflicted immeasurable agony on "himself" countless times.
Angier tests out drowning in his bathtub after Julia's death—because of the Anachronic Order, he might be trying to see what drowning feels like in case he winds up in the glass case, after he's already come up with his trick, but he may also be trying to learn if Julia actually had suffered while she was dying.
One wonders what the London police will think of the warehouse after the film's events (if the fire leaves enough evidence for an investigation): the burned remains of the presumed-dead magician Robert Angier, shot by an unknown assailant... and surrounded by dozens of corpses whose fingerprints, blood type and appearance show that EACH of them is Robert Angier.
More importantly, one can only brace themselves for what is bound to eventually happen if the machine survives the fire fine and working...
, each time Angier uses Tesla's device, a perfect copy of himself is executed. From the dying clone's perspective, he's the Angier who set up the trap and survived all of the traps except this one, while the one who survives remembers surviving every single trap. Angier has no idea and no way of knowing whether the consciousness that pulls the lever is getting executed or surviving each performance.