When Eldon returns to the office to "clean up his mess", he confronts the office manager. Upon entering the office, Eldon closes the door. When you see the close up of Eldon pulling his knife out, you can see the door is open and into the hallway. A moment later, just as Eldon is stabbing the office manager, the door is closed again.
The cuff with which Sam and Dean chain up Eldon is so big (evident also in the shot of the left-behind arm) that he could in fact just have slid his hand out of it. Throughout the scene when he is supposedly chained up, David Hoflin very obviously holds his hand in a position intended to mask this.
Eileen MacCormack comes in to the study because she has perfect 20/20 eyesight. Yet her lids appear to stay wider to avoid contact lenses and in the close up of her face, there appears to be a line on the white of her eye and on the iris of the other eye, where the edge of a contact lens would be.
Sam meets Charlie on the side of the road, arriving in a beat up subcompact with a Kansas plate on the front. While common throughout the show, Kansas only issues a single vehicle license plate, to be displayed on the rear.
When Sam and Dean capture someone they always restrain both their hands, and almost always tie them to a chair as well, because this makes it very difficult for them to escape. Yet when they bring Eldon back to the bunker they not only allow him to stand, they only restrain his left arm. Sam and Dean are experts at holding people against their will as they have to do it all the time in their line of work, they would of never made such a sloppy, amateur mistake like this.
Charlie should not of stayed dead, now that Castiel has his own grace back and is once again a fully powered Seraph he has the ability to resurrect people.