Corrected entry: Olivia brings Angier the notebook of Borden and Angier realizes, that it is encoded. "Even with the keyword it would take months to decode it." Furthermore, he admits to Allie in the Colorado Springs restaurant that the cypher changes with each day and is "time consuming to translate". However, after Angier received the keyword ("TESLA"), he can be seen several times reading the notebook in a speedy manner as if he already decoded the whole book. Nevertheless he reacts surprised as if he has never seen the entries when he should have, namely WHILE DECODING the book. The book he reads is actually the original notebook from Borden, not the one he uses to transcribe the translation, which is smaller.
Correction: You're basing an awful lot on the statement that Angier is seen reading "in a speedy manner as if he already decoded the whole book. That's quite a big assumption and assumptions rarely form a good basis for a mistake. The simple fact is that there is no concrete evidence that Angier has done any such thing; all the evidence in the film points in the other direction - notably Angier's own statements about the difficulty of the cypher meaning that months would be required to decode it and his evident shock [and subsequent anger at Tesla] when he finally unscrambles the last entries. Decoding the cypher is, as Angier states, a time-consuming business; any sequences involving Angier reading fast can simply be taken as him reading a newly decrypted entry in its entirety, or even reviewing old entries for anything that he might have overlooked, or looking for new revelations in the light of additional information.
Corrected entry: When Angier asks Nikola Tesla to make him a machine for his magic act, Tesla makes a machine that can exactly duplicate human beings, down to their memories. Why would Nikola Tesla sell this machine to a lowly magician when it could be sold to his government for colossal amounts of money?
Correction: How is this a mistake? Tesla's motivations are his own - just because YOU feel that he should sell it to the government, it doesn't make it a mistake that he chooses to honour his deal with Angier, who, as we see in the film, is considerably more than just a lowly magician and undoubtedly compensated Tesla very well for his work.
Corrected entry: When Robert performs his 100 shows with his magic trick, he (or his clone) dies in the water tank and the other shows himself to the public above the audience. But when Alfred is backstage and tries to save Robert, the 'other Robert' does not show himself to the public. How does this person know there were troubles backstage? When the trick goes correctly, he shows up within seconds. At that point there wouldn't be enough of a commotion from backstage to tell him their plan had been carried out.
Correction: The "original" Angier sees Borden come up on the stage to examine the machine up close. He then assumes, correctly, that Borden will be sneaking behind the stage to find out more about how the trick works. He then knows that this is the night to put his plan into action (this is, after all, what he's been waiting for, that Borden would try to steal his secrets). When the clone Angier is created, he has exactly the same memories as the original, so he knows about Borden's spying and that the water tank is in place. He then hides away, leaving only one dead magician and one murder suspect.
Corrected entry: When Angier is shocked by Tesla's fence and falls down, his watch falls out of his pocket, but in the next shot it's back in.
Correction: Not true. The next time we see him, his watch is lying on his stomach. As he rolls over and gets to his knees, it falls off and dangles from the watch chain. We then see Andy Serkis for several seconds, in which time Angier has plenty of time to rise to his feet and tuck his watch back in its pocket.
Corrected entry: During the first trial scene Cutter states that he witnessed Borden simply "watching Mr. Angier drown". It is clear ,however, that Cutter witnessed Borden trying to save Angier from drowning as He is seen in the backround when Borden is attempting to smash the glass tank.
Correction: Borden didn't react immediately when he saw Angier drowning–he was shocked and took a few seconds before reaching for the axe. Cutter might think Borden reacted only after noticing him.
Corrected entry: If Alfred's twin was produced by Tesla's machine, Alfred would have understood Danton's trick immediately and had no need to sneak back stage and fall for the set up.
Correction: Alfred's twin was never produced by the Tesla's machine, he was his real biological twin. Alfred never actually had Tesla build any kind of machine for him, it was all a ruse to throw Danton off track.
Corrected entry: The use of Angier and Borden as plants for the water tank trick at the beginning makes no sense; they never wear any kind of disguise (except changing their clothes), so all it would take for the technique of the trick to become known would be for someone to see the show more than once, which would doubtless happen at some point.
Correction: They didn't wear any disguise that time, but that doesn't mean they always do so.
Corrected entry: Cutter knows about Angier drowning his clones and even helps him with the 'trick' by preventing Borden from smashing the tank. Why, then, is Cutter so shocked to see Angier alive after he comes home from the jail?
Correction: Cutter does not know about Angier drowning the duplicates. Angier makes sure Cutter doesn't know by telling him he needs his help "out front" to keep him away from the backstage area when his duplicates are drowned. Cutter honestly thought Borden had set the tank up to drown Angier and, upon seeing Angier already dead, Cutter stopped Borden from making a huge mess.
Corrected entry: Robert Angier's real surname is Caldlow, but he's married publicly to his wife Julia under his surname of Angier. Later on in the film after Julia's death, when Angier meets up with Cutter and Cutter explains why he can't get any work, Cutter says that nobody wants to hire the man "who killed Julia MacMillan on stage". Wouldn't she have been Julia Angier at that point?
Correction: Since Cutter and Angier were audience plants during those shows, it's not unlikely that Julia would've went by 'MacMillan' - either her maiden name or a stage name - to dissociate herself from her husband while performing.
Corrected entry: The box used to drown Angier's clone has glass sides, but they serve no purpose, other than to reveal for the camera what is happening inside.
Correction: Not so - there are numerous possibilities - a magician ordering multiples of that box wouldn't raise suspicion; he needed to confirm the clone died (he thought drowning was a merciful death); he kept the glass cases uncovered as a reminder to himself of the price he was paying. Not a plot hole. It is also the tank used earlier for each performance, which is hauled offstage and below, so no suspicion is raised with it being there.