Deliberate mistake: Very often, during Skype or other video chat conversations, the people on the computer screen look left or right when talking to someone who is not directly in front of the screen. Although it certainly helps the viewers understand who's talking to whom (which is why I assume it's a 'deliberate mistake'), it isn't realistic, since it implies that the people on the screen are actually constantly looking away from their computer instead of at their screen or webcam.
Deliberate mistake: Whenever anyone walks across the front hallway, it takes them 6-7 seconds to walk from one stairway to the other. On the backside of the stairway, it only takes 1-2 seconds to walk across.
The Grasshopper Experiment - S1-E8
Deliberate mistake: At the end, Penny holds up a bottle of rum to show Leonard that she added it to his drink. However, the B is missing from the name "Bacardi" (00:19:30)
The Retraction Reaction - S11-E2
Deliberate mistake: Leonard is on NPR on a Friday, and the guys don't talk about it until the following Monday at work. They spend so much time together, they surely would've discussed it sooner.
Answer: Because Raj's selective mutism seems to be caused by women that Raj sees (on some sort of conscious or subconscious level) as a potential sexual partner. An attribute that wouldn't apply to either his sister or mother.