1969 - After Dr Sayer exits his car he looks up at the care facility he has an interview appointment. Clearly heard in the background is a modern day electronic siren at a time when the Federal 'Pulsator' siren was still the standard siren used.
When Dr. Sayer takes Leonard out into the city for the first time, they see (among other things) an aircraft landing - a Boeing 747. The movie takes place in 1969 and the first revenue flight of the Boeing 747 was January 21st, 1970. Additionally, the 747 is in El Al livery that was used around 1990.
Dr Sayer puts on a record saying "This is one of the most beautiful arias ever written...". The record is clearly an LP (you can even see "Long Playing" on the label) but it starts turning at 78rpm - and the music is heard at normal speed.
When Leonard gets the correct dose of medicine and 'awakens', he walks with almost no difficulty. If he had been catatonic for years, and even if he had been exercised regularly, he would not have been able to just get up and walk around so easily. His muscles would have atrophied. His voice would also have been raspy from disuse.
Both times through "Slumber Boat" (Riley and Gaynor, 1898), Leonard's mother substitutes the first half of the second verse ("Baby's fishing for a dream") for the second half of the first ("His line a silver moonbeam is").
When Dr Sayer first arrives at the facility he remembers to retrieve his paperwork from the car. Then he locks the door, but leaves the keys in the lock. Next he places his hand in his pocket as if pocketing the keys.
In the parking lot scene just before Eleanor tells Dr. Sayer she believes his theory, Dr. Sayer gets in his 1964 Dodge Polara that has a pushbutton transmission control. When the car is shown from the outside, it has a column mounted shifter used only on 1965 and later Dodge cars. Also, to shift from park into reverse, the shifter should have been moved down instead of up.
Dr. Sayer's coat is unbuttoned when he caught up with Nurse Eleonor Costello at the stairs of the hospital, then when he asked her out it is buttoned. When they descended the stairs it is unbuttoned again.
When Dr. Sayer begins to type up Lucy's initial diagnosis, he puts a new form into the typewriter and begins typing. After only a few clicks, a close-up shows him already halfway through his second line of typing.
Dr. Sayers takes the group to a dance hall. He is sitting at a table and eats the cherry that was from his drink. A woman patient pulls him to the dance floor but the cherry that he ate appears on his napkin.
When Nurse Costello approaches Nurses Margaret and Beth, Margaret says, "The patients have all been given their morning medication." The program the nurses are watching is "Days Of Our Lives," which in 1969 was broadcast at 2PM in NYC; well into the afternoon.