The snow that was used for the snowballs was artificial, and did not cooperate well. According to Kaling, the snowballs would "'explode' before they made contact".
When Jim refuses to let go of Dwight's hand while shaking, you can see and hear Stanley laughing in the background.
Kaling purposely made Dwight "complicated" and "mean" in the script; she wanted to avoid a situation wherein Jim and Dwight become best friends, calling it something that would happen in a "crappy sitcom feel-good formula." She wanted to stress the fact that "Jim and Dwight are not friends. Kaling specifically wrote Jim to be "off-guard and surprised" in the episode, because she reasoned that "perfect isn't always nearly as fun to play or watch as flawed."
It is implied that Kevin, an accountant, doesn't know what a comptroller is. Comptroller is a fancy name for an accountant, or a financial officer of some management level.
According to Kaling, the group had to pretend like it was cold during the outdoor scenes when it was actually warm.