What exactly is story continuity?
For many, it is just a simple route from point A to point B and everything occurs as a smooth road.
But, in reality, there is more to that than meets the eye and sometimes it is very subtle. For instance, the following scene from a book which takes place at the end of 1950:
Billy sat on the floor, watching the Roy Rogers Show on the huge screen. Nellybelle, the Army-green jeep, was, once again, driving away without Pat.
There are three inconsistencies in the above two sentences...
1) maybe some people would consider a 10" screen huge and in 1950 maybe it was, but...
2) color on TV didn't happen until late 50s and then, only the rich had it. Most Americans didn't have color TV until the 60s.
3) this is the most subtle, The Roy Rogers Show didn't air until 1951.
Other inconsistencies which can harm continuity are simple actions. I wrote a tale where two riders were preparing to break camp and get on their horses. I had the one getting on, off, on, off, on, off. As my alpha-reader stated: I'm getting light-headed. Just let him wait until everything is done THEN let him get on his horse.
In a current work, I have an accident happen and the father says: "Daniel, you go to work. Rachel, you help get the kids around and ready for school."
Off-hand it seems okay but there is an issue. Daniel is a student also. School is out and it is Daniel's first day at work. Needless to say, there was a little scurry to straighten out the scene. FYI: Daniel went to work. Rachel got the kids around and they worked in the garden. Whew!
Writing period pieces, whether historical or not, get tricky. With time, things change. So do holidays!
Presidents' Day, Memorial Day, and Columbus Day weren't always on a Monday. In fact, Veterans' Day, observed November 11th was temporarily changed to a Monday and then returned to its proper place where it is now. Still, if you are writing a period piece, the writer must make an effort to be true to the era. Three-day weekends were a rarity in the 50s and 60s unless the specified date fell on a Friday or Monday. There was no Presidents' Day - George Wasington and Abraham Lincoln both had their own day of honor.
Also, some holidays have been added to the calendar. Martin Luther King Day was not observed until 1986. To close a school or business on a Monday in 1963 would be breaking your reader's continuum.
Susie sweeps and cleans the floor. She doesn't clean and sweep the floor. If your character slips to the floor and somebody helps her to a chair. Obviously she can't lean over and rest her hand out on the floor to prop her up.
Continuity is more than getting a person from point A to point B. It is about making sure everything in between is in correct order also.