Joel interrupts Ellie at most an hour after she was in the process of getting a new tattoo. When he inspects it, her skin is fully healed, though still baring her old burn scar. In reality, a fresh tattoo would cause the skin to be bloody and inflamed.
Bone dust can have negative health effects when breathed in, yet Joel is not wearing a breathing mask while grinding down the bone for the saddle on Ellie's guitar. However, many hobbyists will ignore best practices regarding use of personal protection, especially in a time when such things are not readily available.
The cans of beer that Joel and his father are drinking are current opening style. In 1983 these would've been ring pull cans.
While Joel and Ellie ride horseback along the trail, a crew member can be seen in tall grass on the left at 34:50.
The Apollo 15 Command Module is actually kept in the US Air Force Museum in Dayton, Ohio.