Mary uses a LED lamp when reading her book. They didn't exist back then.
The end credits note the character played by John Hartman as "Dr Goetsch". However, the establishing shot for the counseling visit by Sheldon and his mom shows the window of the office, which says, "Jeremy Goetsch, MS - #1 child therapist in the Pennysaver". The academic degree "MS" (Master of Science) indicates a therapist (as noted on the window), not a psychologist (PhD or EdD) nor psychiatrist (MD) and does not entitle the professional to be officially called "Dr".
In the therapist's office, Sheldon asks about Dr Sturgis, ending his question with a preposition. Sheldon wouldn't likely make such a grammatical error.