When Tilly arrives in town, she's carrying a case for a manually operated Singer sewing machine. Later on, when we see her at work, there's no handle on the side of the machine and she's clearly using both hands to guide the fabric. The Singer was operated by a knee lever that stored within the case when closed and then was pulled out and slotted into the bed of the machine leaving both hands free to guide the fabric. Very portable for the era.
When Tilly walks out to the sports field in her black dress she takes off her gloves, one at a time. She is no where near Molly, yet when she sits down, is seated next to Molly without moving an inch.
When Evan is clipping a newspaper photo and is startled by the clattering of a golf ball on the roof, the long shot shows he has cut roughly one-third of the way across the top of the photo when the ball hits, but in the immediately following close-up shot showing his reaction (wherein the scissors turn and cut off the top of his head in the photo) the remaining two-thirds of the paper above the photo are shown as having been cut. There was no time between the golf ball noise and his errant snip for him to have finished cutting across the top of the photo.
Tilly is carrying a Singer sewing machine by the handle on the top of the case. These machines were not designed to be carried that way - the handle is just to lift the case on and off. In addition, the case is only meant to cover the machine, and the cover's clips are not strong enough to hold the heavy machine, and would fail.
The fire follows the fabric down the hill to the town, yet when we see the charred aftermath, there are long remnants of unburned fabric on both sides of the fire trail running down the middle of the fabric. There was a liquid accelerant used on the fabric and the flames spread to the grass on either side of the fabric. The only way the grass and fabric would not have burned would be if the fire was put out by the crew.
The wisteria on Molly and Tilly's front porch appears to be blooming. It is impossible for blooms to be on a lifeless vine in a dusty, desert like place. The blooms are fake and so is the vine. The vine lacks the twisting nature of wisteria.
When Teddy goes to hit Evan in the face at the wedding reception, his fist doesn't actually make contact with Evan's face, but he falls down anyway.
In the scene where ( grownup) Tilly is in the classroom with the teacher, the alphabet on the top of the blackboard is missing the letter "R".
When Gertrude passes the book of stage costumes to Tilly ( at about minute 93), you can see that the cover reads "Soldiering On", which was a dark red book issued to members of the Australian Army after WWII. In the next shot the fake cover is on the book.
When Tilly bribes Sgt. Farrat with the feather boa in front of the petrol bowser, it can be clearly seen to read "cents per gallon". In 1951 dollars and cents were still 15 years in the future. It should have read shillings and pence per gallon.
In 1951, the characters talk about being children (in 1926) and playing at Superman. The first Superman comic was not published until 1938.
The record cover for South Pacific is the original Broadway cast recording (1949), but the excerpt from "Bali H'ai" is from the 1958 Film soundtrack. Similarly the excerpt from Oklahoma is from the 1955 film soundtrack. In both cases these post date the scenes in which they occur.
The action takes place in 1951. At the town dance, before Trudy walks in, the band is playing 'Ballad of a Teenage Queen', which wasn't written until 1957, and was a hit for Johnny Cash in 1958. (Wikipedia)
"Meet Me With Your Black Dress On", originally recorded by Jimmy Nelson, was released in 1952, while the movie is set in 1951.
This is a small town with adults of various ages, yet there are no children to be seen, except Teddy's siblings.