Continuity mistake: When Eddie is hiding with the golf club, there is a blue chair which got knocked over during the murder. But a few minutes later when Eddie is peeking round the corner to check for intruders, the blue chair is magically standing upright again.
Plot hole: If Bradley Cooper was able to "quintuple" his money every day in the market as he claims to have done, he would have been able to earn the $100k he borrowed from a loan shark within a few days, starting from $800. Alternatively, he is shown in one scene winning a pot in poker where he could presumably also make a large amount of "seed" money from gambling. There was no need to borrow such a small sum of money from a loan shark, making the entire sub-plot unnecessary.
Factual error: During the shootout in the apartment, the blinded henchman fires his handgun 24 times before reloading (and about the same afterwards). Only small-calibre pistols would have that capacity, and the gun he's using isn't one (either to look at and from the bullet holes it causes).
Factual error: Immediately after Eddie surfaces following his dive, he rests with his head well above the water. Had he actually been in water deep enough for the dive, he would have floated with his chin about even with the surface.
Factual error: Eddie claims it takes 30s for the drug to take effect. Tablets/capsules do not work within 30 seconds after ingestion. At most, 15mins is the time a drug can be absorbed into the body. This is also noted in the movie reviews.
Continuity mistake: The morning of the second meeting with De Niro we see Bradley Cooper's knuckles are bloody from the fight in the subway. At the meeting his knuckles are fine and afterwards they are bloody again.
Other mistake: When Eddie leaves his soon-to-be murdered friend's apartment, the apartment door automatically closes behind him. However, when Eddie returns, the door is ajar. It wouldn't be ajar if it were an automatically closing door.