The helicopter shown right before the scene with the baby Patrick is a Bell Jet Ranger. They did not exist in the Military until the Johnson Administration.
In the scene between Jackie and her assistant Bess in the car following their pre inauguration visit, there are several indications that this movie was filmed in the early 80s. First, if you look over Blair Brown's right shoulder as the car moves down the street, you'll notice a current version of a "Do Not Enter" street sign. It's the kind with the big red circle with a white line going through it. Those type of street signs didn't appear across America until the 1970s. As the car continues to move down the street, immediately behind it are a few other automobiles from that time period. However, again over Blair Brown's shoulder, you'll notice the car passes several 80s era vehicles which are parked.