When Sheldon is being driven to school in his mom's station wagon, the ignition switch is clearly in the off position.
Young Sheldon has blue eyes whereas the adult Sheldon has dark brown eyes.
When Sheldon states that he would not touch his brother's ha d until 17 years later "thanks to the invention of Purell." This implies that it was invented in 2006 based on the plot taking place in 1989. However, a simple Google search will state that Purcell was invented in 1988, one year before the statement would have been made.