In the meal Lydia has with Andris, the amount of food on his plate changes without him eating and the knife on the plate shifts position.
When Tàr enters her house, her friend says "I cannot find my metropolol." The name of the medicine is "metoprolol". Somebody who uses this regularly knows this.
When Lydia is talking to the two technicians after a rehearsal in Berlin, she requests they send her audio and video recordings, but the console in front of them in the booth is actually for controlling lights, not audio/video.
When Lydia is looking at Twitter, she is tagged in a tweet from two minutes ago that has over 1,000 re-tweets. The sidebar indicates she only has one new notification.
At about 1 hour 45 minutes, when Lydia drops off Olga after their practice, she is driving a Porsche Taycan, which is a silent electric car, but when she drives away the sound of a gas internal combustion engine revving is heard.
References to Apocalypse Now suggest the final scenes of the film are set in the Philippines, a right-hand traffic country. However, when Tár goes to receive her massage, traffic in the background can be seen driving on the left.
The title character states to students that Alma Mahler left Gustav for Gropius, and that the 5th symphony was dedicated to her. In fact, Alma stayed with Gustav even after Gustav became aware of the affair. Also, while the Adagietto was written as a love letter to Alma, the 5th symphony was not dedicated to her. Mahler's 8th symphony was dedicated to her.