When Mary does her home pregnancy test, it's the middle of the day. Back then, you had to use your first morning urine on those tests to assure accuracy.
There is a wooden Texas shaped plaque hanging in the school where Sheldon's dad works. It displays the State Universities of Texas. Sheldon is set in the late 80's or early 90's. On the plaque, you can clearly see "Texas State" south of Austin in San Marcos, TX. Prior to 2003, "Texas State University" was named "Southwest Texas State University". The name changed in 2003.