When Leonard and Penny are at the shooting range, Penny puts the magazine into the gun and never puts any ammunition into the chamber. Meaning that Leonard could not have shot himself in the foot.
Penny cycles the slide on the handgun before inserting the magazine. To make the gun ready to fire the slide needs to be cycled after the magazine is inserted.
When Penny and Leonard are at the gun range, a man in a blue T shirt not wearing hearing protection walks behind them and through the door. No gun range would ever allow this to happen while people are firing weapons because the concussive forces of the gunshots bouncing off of the concrete walls would be unbearable and cause permanent hearing loss.
In the gun range scene, the shooter in the booth next to Penny and Leonard is firing a semi-auto pistol, but when he shoots (twice) no shells are ejected from his firearm.
At the end, Sheldon Says "Ich bin eine Bavarian." The correct German is "Ich bin ein Bayer." Bavarian is the English word for a resident of Bavaria (Bayern). However, it is clear that both he and Amy are paraphrasing for others who wouldn't understand the actual German words. (After all, Amy clearly says "pretzel" when the German word for it is "brezel".)
There are only one non-rectangular national flag in use in the world; The Nepal flag (as Sheldon has mentioned). The Swiss and Vatican flags are actually squares, which is often mentioned as a 'non-rectangle', but a square is still a rectangle (all squares are rectangles, but not all rectangles are squares).
The Ohio Burgee (a "swallowtail" flag) is not a NATIONAL flag, otherwise all the regional, county, city flags and coats in all the world should be considered.
In the opening of "Fun with Flags" Sheldon states, "unlike the flag at Fort Sumter, I am still here". He should have said Fort McHenry, as mentioned in the National Anthem. "...our flag was still there." Sheldon says "like," not "unlike." He is not referring to the flag at Ft. McHenry as mentioned in the National Anthem, but rather the flag at Fort Sumter which was raised on April 14, 1865 as part of the celebration of the Union victory - it still stands today.
It seems unlikely that an intelligent scientist (Barry Kripke) wouldn't realize that firstly, he speaks with an articulation disorder and secondly, that this is the reason Siri won't work for him with speech recognition. However, it's established by this point in the series that Kripke is unaware of his speech disorder and denies its existence. (In a later episode he refers to his speech disorder.)
While speaking to Raj in his office, Sheldon states that the flags of Liechtenstein and Haiti were identical by coincidence; a fact that wasn't discovered until they competed against each other at the 1936 Olympics. Haiti participated in the 1936 Olympic opening ceremonies, but did not compete after its lone athlete withdrew from competition.