One of the newspaper headlines on a table is dated in mid-October 2018. Later in the film, on Day 473, the mother is writing on an October calendar as she keeps track of her pregnancy vitals. Assuming Day Zero was near mid-October 2018, then Day 473 should have been in late January or early February 2020.
Taking blood pressure measurements during pregnancy is very important and its inclusion in the film was a good detail. However, when Blunt's character is taking her blood pressure, the blood pressure cuff is too low on her arm and she is not using the stethoscope to record the pressure. Given that using the stethoscope greatly improves the accuracy and makes taking the measurement easier, there was no reason that she should not have used the stethoscope.
Inaccurate "Factual mistake": blood pressure cuff and meter can reasonably be used without a stethoscope. Highly trained medical professionals know how to do so. And less efficient medical professionals have been able to obtain a reading without the cuff being in the optimal position. The commonly used Doppler would be heard by the monster.
While pregnant, Evelyn uses a stethoscope to listen to the baby's heart in the womb. This may be difficult with a regular stethoscope but not impossible. There is a specialized type of stethoscope called a fetoscope which is simply a different shaped stethoscope but functions similarly. A doppler is more commonly used in today's hospitals to hear the fetus' heartbeat. However, with effort, a regular stethoscope can hear a fetal heartbeat.
Lee takes his son to the waterfall to note that loud natural sounds can mask their noises, with both yelling to demonstrate. If Evelyn was so far along in her pregnancy he should have set up some kind of camp there so that any screams from the childbirth could be masked.
The corn plants in the fields are green at day 472. This means they were planted in the current season. They have a full silo of corn, so there is no reason they would have needed to plant an entire field of corn to feed their small family. Also the perfectly aligned rows imply that they were planted by machine, which would have been extremely loud.
The opening scene takes place on "Day 89", while the remainder of the film occurs on or after "Day 472", or one year and 18 days later. But days 472 and beyond clearly occur earlier in the fall than day 89. As is noted in the "Trivia" section, the opening scene was filmed last because it required John Krasinski to shave off much of his beard, so it was indeed shot later in the fall. This anachronism could have been corrected by changing "Day 472" to, say, "Day 442".
In the fireworks scene, the (first) fireworks are supposed to be high in the sky above a cornfield, and the camera shot is from ground level (looking up). But you can see that the filmmakers simply superimposed fireworks over the cornfield, as the streamers are clearly in front of the corn plants.
The goof items below may give away important plot points.
Seems very unlikely that no one in the government, especially any of the genius level scientists working for them, figured out that the best way to repel a creature with extremely sensitive hearing was to expose them to an extremely loud or high pitched sound.
When the monster went into the basement after Evelyn, not only would a being with super-sensitive hearing hear her panting, it would also hear the two heartbeats, one of the mother and one of the unborn child.