Around 0.02.24 (hh.mm.ss) into this movie there's a close-up of the picture just drawn by Gail Beechum (daughter visiting her father Frank on death row. It's just your bog-standard green field, fence on the horizon, and a blue sky with a sun and four birds. It's clearly signed "GAIL" in childish scrawl.
We've seen the same picture earlier in the visit, at 0.48.12, before Gail has coloured in the field. She'd dropped her green crayon in the parking lot, and the movie uses this to show how solicitous the prison staff are (they go and find the crayon during the visit).
Immediately after that first sight of the picture, we cut to Evert (Clint) interviewing a witness in a cafe, where the cafe wall has a mural of much the same picture (not signed, so far as I can see, but not apparently a child's work). I can understand this as just a fairly meaningless "linking device".
Later Evert searches the apartment of Michelle (his journalist colleague who died in a car accident at the start of the movie). At 1.29.09, Michelle's friend produces a very similar picture (again, crayon-drawn green field and blue sky, but this one has a couple of "stick people" and no sun or birds). This second picture is clearly signed "GAIL" in the same hand, probably with the same actual crayon as the first, but the friend says it's something Michelle herself drew when she was a child.
Within the context of the story, I suppose it's feasible Michelle might have visited Beechum before she died, at a time when his daughter was also there. But it would stretch credulity to suppose Gail gave an earlier picture to some journalist in such circumstances.
What possible rationale could be involved here? Is it just a complete lapse by whoever was responsible for continuity? I just don't see how several people working on the film could fail to notice, but I can't figure out why it would be done deliberately.
