Continuity mistake: When Nina and Leroy are standing halfway up the stairs as he is about to announce that she is the new star ballerina, they both hold a glass of champagne. At first, Nina's glass is almost empty; at the end of the scene however, she is holding a full glass.
Visible crew/equipment: In the scene when Nina arrives to her home after she knew she was chosen, she is looking for her mom (who bought a cake for Nina), and there is a camera man in a mirror.
Factual error: In the scene where Natalie Portman travels from her house to Lincoln Center she is riding the 1 subway train. The model train shown is a R142, which only serves the 2,4,5 trains. The one 1 train line is actually served by the R62A.
Factual error: Toward the end after Nina dances the black swan and she's in her dressing room, Lily knocks on the door to congratulate Nina on her performance. When Lily turns around to leave, her huge double-wing tattoo is visible on her back. No ballet company will allow a dancer to perform on stage with tattoos that have not been properly covered up.
Other mistake: When Nina and Lily are at the bar, it shows Lily move to the seat directly to Nina's right, thus placing Nina on the right side of Lily. However, the entire time they converse, Lily's eyes are looking to her left. Same goes for Nina who is looking to her right the entire time.
Continuity mistake: We see Nina put on red lipstick on the subway. In the next scene, when she's in the studio, her lips are skin-colored, implying that the lipstick is off. But when she enters the director's office, the lipstick is on again, even though she never reapplied it.
Other mistake: When Lily and Nina are at dinner, Lily is surprised that Thomas calls Beth "Little Princess." This shouldn't be new to her since he addressed Beth as "Little Princess" at the gala where he announces Beth's departure and introduces Nina as the Swan Queen.
Continuity mistake: When Nina watches Lily dancing after filling up her water bottle, look very closely at Lily's back as she spins around and you can see that her tattoo isn't there. As she was wearing a vest and her hair was down over her back, it is likely the film makers thought they could get away with this.
Answer: **Spoiler Alert** I would say you are correct about the movie being a metaphor for descent into madness, but also displays themes of repressed sexuality and transformation. As the main character is given the lead role, she must play dual roles, one good and one evil, with the hallucinations representing the latter. Towards the beginning, Nina only embodies the personality traits of the white swan, innocence and grace. As the film gradually progresses, Ninas hallucinations represent her metamorphosis into the seductive and mysterious black swan. The film expertly convinces the audience that Lily (Mila Kunis) is out for Nina's role. In a twist ending, it is revealed that Nina has imagined most of her encounters with lily (including their sexual one) and has instead been battling herself, such as breaking away from her domineering mother and coming to terms with her sexuality. At the end, Nina really does stab herself (but actually hallucinates it is Lily she is stabbing) and her fate is left ambiguous.