In a postmortem a doctor states that a specific woman who is supposed to be a mother cant be a 'Mrs' because she is a virgin, or at least he is guessing she is. However the title 'Mrs' refers to marital status, not parental status or virginity, and women can obviously have children without sex via fertility clinics etc.
The final shot at the parade shows the parade continuing behind the lone body of the shooter, this after multiple cops had subdued him and surrounded the corpse. The body of a dead criminal would never have been left unattended for even a second, and a parade would certainly not continue after a massacre such as what had just occurred.
There are several headlines in the newspapers regarding the killings, but the articles underneath the headlines do not pertain to the actual headline.
The car in the flashback scenes was a 1951 Chevrolet, with post-1973 New York State license plates and registration. Briefly, it also turns into a 1939 Plymouth, when it hits a pothole.
A shadow from one of the crew, most likely the camera operator, can be seen on Peter and Casey in bed.