In the ice cream shop when telling the story of how he caught his dad with another woman, the position of Sheldon's spoon changes between shots several times.
There is no feasible explanation for Raj, having to stand up on the steps to enter it, not noticing Stuart's body in the hot tub, even with the bubble jets running. The lights are on, and the bottom of the tub is a light, contrasting colour.
When Penny & Sheldon are driving in the car and picking apart their significant others, Penny is complaining about Leonard's nose whistling really loud one night as he slept. Sheldon replied, "Have you ever noticed that it's always in Ab (A flat)? Penny asks, "Really?" In an attempt to prove it, he whistles in a supposed "Ab," and she becomes convinced, but he's actually whistling a half step down, in the key of G.
Stuart claims to be nude in the hot tub, but neither his swim trunks or street clothes are visible on the deck in the 'over head' view as seen from Howard and Bernadette's POV in the upstairs window. While this could mean he dis-robed in the house and walked outside naked, that seems out of character for the "low self-esteem" Stuart. And if that were the case, Raj would've seen the clothes on his way through the house, so he would not have been surprised by Stuart's presence.
Even with the jets on, Raj would have noticed Stuart wasn't wearing trunks. Stuart's pasty complexion would make even a flesh-coloured swim suit stand out in contrast.
Sheldon says that the origin of his 'knocking three times and saying the person's name' behavior goes back to an incident in his childhood. However, in the early episodes he had yet to develop the habit.