The movie is set in the 1930s, at one point a character is loading a shotgun with plastic shotgun shells, but plastic shells weren't introduced until the 1960s. During the period of the movie shotgun shells were made of thick paper with a metal bottom for the primer.
Telephone (utility) poles shown in several scenes include both telephone lines and cable TV lines, some of which include modern "expansion loops." Cable television wasn't introduced in the US until 1948.
When Bertha puts on the dress that Jack gives her, she asks how she looks. Jack gets out of the car and is staring at her smiling. During a close up of his face, Jack then says "Come on.", though his lips never move and he's still smiling.
The flowers at Cricket's funeral (ranunculus, wax flower, French anemones) would likely not have been available in the rural mountains of Virginia at the time. They would have likely used wildflowers such as goldenrod and queen anne's lace.
Heavy kudzu growth is visible in many scenes - this is an invasive plant species introduced to the United States in the early 20th century, and it's much more common in Georgia where the film was shot, than Appalachian Virginia where the film was set. And it probably wouldn't have been in either of those areas at all in the 1930's.
The goof item below may give away important plot points.
During the shootout at the bridge, the sheriff shoots Agent Rakes, seemingly in the back of his left leg. But when Rakes retreats to the bridge, there is no sign of a bullet-hole or blood anywhere on the back of his suit.