Sheldon generally can't stand someone entering his room, yet he lets Martha in. However, his hesitation and the "audience" response upon approval suggest that this isn't a goof, but a deliberate plot twist showing that Sheldon likes Martha so much as to allow her to be in his room (providing that he himself is not there).
At 9:05 Sheldon says the Green Lantern oath as In Brightest Day, In Darkest Night..". The current version of the oath starts " In Brightest Day, In Blackest Night...", but the original oath as said by Alan Scott was "Darkest Night". Sheldon may like to stay with the original because he hates change, or maybe he just prefers it.
Raj states that he rented the 4 hour version of "Watchmen". The longest version of the film is the 3.5 hour Ultimate Edition. Also, the DVD Raj is seen holding is that of the 3 hour Director's Cut.