When Ted gets stuck out at the solar farm, they build a fire that night before they go to bed. The next day there are no ashes or place a fire was built as they are waking up.
(at around 21 mins) Charlie is shown pouring liquid onto one of the keyboards in the conference room, causing the computer to begin to act up. If you pour liquid on a keyboard it might fry the keyboard but would not have an effect on the computer or the monitor, especially if the actual computer is in another room, as we are told it is by the tech officer earlier in the show, when he says that he will set it up so they can access Amir's computer in the conference room.
One of the main plot points involves getting to Level 10 in the game "Prince of Persia." In reality, this game does not have numbered levels.