If Dease was committed to a mental institution for pleading insanity in his father's death, he would not be released after his recovery, but retried for his father's death.
Several characters are seen smoking in the galleries. This is a major breach of etiquette in the art world and likely against laws regarding smoking in public (filmed in Miami, there is a Florida statute banning public smoking).
When Morf just finishes hearing voices in the soundproof room the other gallery director informs him that the sound wasn't working, that it's not voices but whale sounds from 20,000 feet under the sea. The deepest known whale dive is less than half that depth.
When Jake Gyllenhaal is at the eye doctors, the settings of the phoropter head in front of his eyes makes no sense. Only eye doctors and optometrists would be able to notice this.
Where Jon Dondon (Tom Sturridge) is filing away the contents of Ray Ruskinspear's private investigative report on Vetril Dease in a filing cabinet, Jon brings out his phone. The iPhone screen display shows an incoming call, yet when Jon swipes over to answer, he instead is leaving a voicemail on Morf Vandewalt's (Jake Gyllenhaal) voicemail.