When Sheldon goes to apologize to Penny, he only knocks once (although he actually raps with his knuckle 3 times).
As with most Pilots to Series, there are some changes in set design in between the first and second episodes. In the Pilot, Penny's "Kitchen" is a wall; starting with the next episode, it is now a full Pullman, complete with dining island.
The noise that wakes Leonerd up is the sound of the front door closing, but when he investigates both their and Penny's doors are open.
In between takes the french toast Penny is holding changes; from being mostly covered with egg to fully covered.
After Penny finds out they were in her apartment during the night, while Sheldon talks to her she first has her left arm on her waist, then after the cut she has both arms on her waist.
When bringing Penny's furniture up to her apartment, Leonard and Sheldon lay the box on the stairs and Leonard states "Now we've got an inclined plane. Force required to lift is reduced by the sine of the angle of the stairs..." This is incorrect, as the force required to lift it stays the same. The force required to push the box up the stairs is half of that required to lift it.
When Leonard responds to Sheldon while they are in Penny's apartment, the window in the background has gray light coming through it, but when next seen, the light is white.
When Penny and Leonard are talking outside his apartment, at the beginning, someone can be seen coming out of the wall behind them.
In the teaser, Leonard says he has "2600 comic books" in their apartment. That many comics would occupy approximately 20 'short boxes', a common storage method used by comics collectors (and, given their low estimation of their own upper-body strength, the logical choice for Leonard to have made, when measured against the much heavier "long" boxes) yet in the entire series, there is never shown that many comics boxes, nor is there ever shown a third room wherein the boxes might be stored.
The morning after cleaning Penny's apartment, Sheldon makes himself a coffee. In later episodes Sheldon does not drink coffee. Specifically The Work Song Nanocluster (season 2 episode 18), when he says "Coffee's out of the question. When I moved to California, I promised my mother that I wouldn't start doing drugs."
While putting Penny's furniture together, Howard complains over how IKEA's assembly manual represents the least imaginative way of putting the parts together. He states that this is why Sweden has no space program. On the contrary, Sweden has a highly developed space program, most notably its research center and rocket range Esrange, which has been used for launching over 700 rockets into space since 1966.
Sheldon suggests that pushing Penny's furniture up the stairs slowly or rapidly makes no difference, because the amount of work involved would be the same. Although the latter is true, as a physicist he would have known that the power input needed (work/time) would be different. A human being can only generate a certain amount of power, therefore pushing the furniture slowly is easier than pushing it fast. Conversely, the slower they work, the longer their muscles are bearing the weight, tiring out their muscles, making more work, something they should both easily realize.
When Leonard approximates the angle of the stairs as 30 degrees, then says that the sine of that angle would be about half. Sheldon incorrectly corrects him to say it would be exactly half. As a physicist, Sheldon would be aware of the concept of error thus the approximate angle would only yield an approximate sine value. However, the sine of 30 degrees *is* exactly half, so Sheldon is right that the calculation is exact, while it could be seen that Leonard is right, saying "about half" meaning that being based on an estimation makes it, too, an estimation.
Both Penny and Sheldon mention Superman "swooping down" to save Lois Lane in the 1978 Superman film, when in fact, he actually flew upwards to save her.