When Penny and Leonard talk while folding towels, she folds a pink hand towel. In the next shot the towel is partially unfolded.
Just after the opening sequence, Leonard is preparing pancake batter. You can see him spilling a lot of it onto the table, but in the next take, there is only a tiny stain instead.
The pile of towels changes between shots. There is a small pink hand towel on a big yellow one, then there is a small pink on a big pink, then it is back to the small pink on the yellow one.
Sheldon hopes he will still have a "GI" (gastro-intestinal, meaning stomach and bowels) as he already swallowed barium. Barium studies are X-rays shot while swallowing the barium to see the movements of the esophagus (food pipe).
Sheldon's cohabitation rider states, "A girlfriend shall be deemed living with, when she has stayed over, A, 10 consecutive nights, B, More than 9 nights in a three-week period. Clause A is made redundant by clause B, given that it is not possible to have stayed over for 10 consecutive nights, without having first stayed for 9 nights in a three-week period, as clause B would be triggered by staying over for 9 consecutive nights.
Dr Stephanie states she can see that Sheldon's larynx is inflamed while actually looking (very awkwardly) at his pharynx. Both characters should know the anatomy of the throat.