Final credits clearly state: "Filmed entirely on location in Kentucky and Tennessee." The IMDb locations page adds Virginia, but not Washington state where several outdoor scenes were set. "Entirely" is an overstatement here.
The doctor Loretta visits comments that he hasn't seen her since he vaccinated the kids in the family for the measles. The first measles vaccine wasn't licensed for use until 1963, long after the time of her visit to the doctor.
Early on in the film, railroad cars (coal hoppers) are shown. They have Southern Railway markings. In reality the Southern Railway did not operate in eastern KY at that time. They should have had Chesapeake & Ohio markings.
During the early Loretta Lynn Grand Ole Opry appearances, drums are readily seen and heard. Full drum kits were not allowed at the Opry until 1974 while these scenes in real life happened in the early-'60s, Lynn's first appearance being in 1962. The only exception to the no-drum-kit rule at the Opry prior to 1974 was for Bob Wills and his Texas Playboys in 1944.
When Loretta is promoting a single at a record store in Nashville in the early 1960s, a Chevy Monte Carlo, about a 1978 or 1979 model, is visible in the background. Late model cars are also seen at other points during the movie.
When Patsy brings out a box of her old maternity clothes to share with Loretta, a tag can be seen on the sleeve of a blouse. (Most likely the garment was purchased at a thrift store and the tag hadn't been removed for the film shoot.)
When Loretta and Patsy return to the parking lot after shopping, and after they drive off leaving Mooney behind, as he is walking through the lot you can see a 1965 Pontiac Tempest among the cars parked. Patsy died in 1963.
The modern "Ludwig" logo on her drummer's bass drum did not appear until many years later. Levon Helm, who played Loretta's father, might have noticed this, since he was the drummer for The Band, a successful rock group of the '60's and 70's, but he was not on set during the filming of Loretta's successful country music singing career
When Loretta comes home from her tour, her husband reveals a car their son Jack Benny had wrecked. It is a 1971 or 1972 Ford. The time is actually about 1969. The song "Coal Miner's Daughter" was released in 1970.
When Loretta is singing "There He Goes" with The Westerners, not only are the bass player's hands not moving, but he is portrayed playing an upright, or "double" bass. The sound being made, however, is clearly from a bass guitar, not an upright bass.
When Doo and Loretta are in the radio station, after the disc jockey said he had listened to the record, it shows Loretta picking up the envelope and handing it to Doo. He lifts the flap, the scene goes to the disc jockey and in the next scene it pans back to Doo opening the flap again, only this time it's licked and sealed with the metal clasp.
When "Doo" is taking Loretta's picture in their home he is using a pot lid to reflect light from a floor lamp. On several occasions both the camera and crew are visible in the reflection of the pot lid.
Prior to her first appearance at the Grand Ole Opry, Loretta is listening to Patsy Cline singing "Crazy", then after her debut she is summoned to Patsy's hospital room where she is told Patsy was injured in a automobile accident. In reality, Patsy recorded "Crazy" a few weeks *after* her accident. In an NPR interview in 2000 one of the studio musicians present that day remarked that Patsy had difficulty hitting the high notes in "Crazy" because she was still sore from her accident.