Fanon Discontinuity: Originally Elektra was just a normal girl who ended up going down a very dark path after the tragedy of losing her father. In the Man Without Fear miniseries showing how Matt Murdock became Daredevil, she's portrayed as having always been a psychopath, hearing voices and intentionally going looking for trouble so she could murder her assailants. In an odd parallel to Selina Kyle's prostitute past from Batman: Year One, this is one part of an otherwise well-regarded series that a lot of fans would prefer to ignore.
Critical Research Failure: At one point Elektra says the sai is "An offensive weapon. For killing." While it can be used as a stabbing weapon, a sai's primary purpose is defensive. It's designed for disarming and breaking swords.
Iron Woobie: Regardless of how you feel about the films she's appeared in, Elektra has not had a good life. She saw her mother murdered when little, grew up with a strict father who put her through rigorous training since childhood, sees her father murdered, mistakenly injures her boyfriend, is humiliated by her father's killer before being killed herself, resurrected by a former sensei only to be kicked out of the school because of her rage issues and became an assassin for hire while still being haunted by her past. And she is never seen reunited with Matt or getting to avenge her father.
They Wasted a Perfectly Good Plot: In the Daredevil film, Elektra was killed by Bullseye. Now, one would believe this is what the spin-off movie would have been about: Elektra would hunt Bullseye down. Combine that with her becoming an assassin solely to have the funds and resources to find, as well as demonstrating more of Bullseye's attraction to her in the first film to mess her up and other connections to the first film and you might have had a decent spin-off. Instead, it's a totally different movie, leaving her vengeance plot unresolved. Likewise, this doubles as a missed opportunity for any more Ham and Cheese and Love to Hate from Colin Farrell.
WTH, Costuming Department?: Elektra's red outfit has been mocked for being a less revealing version of her outfit from Daredevil while being a bright red in an attempt to be closer to the comics. The end result, as one website put it, is basically a "mom's attempt at looking sexy".