When filming the scene where Dr. Sayer and the security guards attempt to restrain Leonard, Robin Williams accidentally hit Robert De Niro in the face with his elbow, breaking De Niro's nose. De Niro later commented that his nose had been broken before, in the opposite direction, and this injury actually straightened it back out.
For the movie Robert De Niro filmed a scene with "Lillian T.", the only surviving patient from Oliver Sacks' book, "Awakenings". She was also said to have been the most outspoken patient in the 1973 documentary about the patients, also called "Awakenings".
Prior to filming, the actors portraying patients studied films of Dr. Oliver Sacks' actual post-encephalitis patients, and Robert De Niro and Robin Williams spent time with Sacks in the hospital observing him and his patients.
At one point a film Steven Spielberg considered directing, before passing it on to Penny Marshall. The time he spent on the project did yield one useful outcome for him: Steven Zaillian's script took several short chapters, each about different patients, and put them together into a linear whole. This brought Zaillian to Spielberg's attention, and he offered Zaillian the similar task of adapting Schindler's List (1993), which ended up winning Oscars for both of them.
Oliver Sacks has been fictionalized into an American neurosurgeon named Malcolm Sayer. However, Robin Williams's portrayal actually bears a very close physical resemblance to the real Dr. Sacks, as he was in the 1960s. (Contributed on the day of Dr. Sacks' passing.)
The trivia item below may give away important plot points.
Dr. Malcolm Sayer, is a fictionalized version of Dr. Oliver Sacks, who both wrote a book and made a documentary film on the effects of L-Dopa on his patients. In this movie, Sayer eventually overcomes his shyness and accepts a date with Eleanor; in his 2015 autobiography On the Move, Dr. Sacks says that (like his fictional counterpart) he was very shy when he was younger, but he was (and is) also gay.