When Meg starts searching for a "chocolate bar" once Sarah's sugar level drops, Sarah says she had already searched in the box and had found nothing. Yet we clearly see standard U.S. Military M.R.E. (meal ready to eat) packages which include a high sugar ration (in the form of, or in addition to, a dessert with the meal itself and sugar to be used with the included instant coffee), when Sarah was first searching.
When the E.S.U. (Emergency Service Unit) team enters the house and clears the bottom floor officer Keeney calls for a "bus" or ambulance to help Stephen. When E.S.U. are called to a scene an ambulance is automatically dispatched with them, there would be no need for Officer Keeney to call.
When the bad guys are taping a garden hose to the propane tank, it's clear the tank has an O.P.D. type valve because of the triangular handle on the valve. Overfill Prevention Device valves have an added safety feature; they will not release propane without the proper hose fitting attached, which will depress a spring loaded valve just inside where the fitting screws in. Fittings like what is on the tank end used on gas grills. A simple garden hose would not release the valve. Therefore, when the valve is opened, no gas would have been released.
Meg Altman breaks the mirror with the sledgehammer then walks over the razor sharp shattered glass with her bare feet. But right as she's about to walk out the door you see she's wearing some kind of 'hidden' protection on the bottom of her feet.
The goof items below may give away important plot points.
Flammable gas (propane, butane) is heavier than air. When the villains try to gas Meg and Sarah out of the panic room, Meg says to "keep down" when this is in fact where the gas would go. Staying close to the floor would increase the danger of asphyxiation.
Striking a flame or spark in the flue when there is a flammable gas mixture in it would not result in flame shooting back to the source of the gas, and even if it did it wouldn't result in the gas cylinder being blasted around the room. At best a continuous flame would burn at the point where the pipe joints the duct (after severely burning Meg's exposed arm); at worst, but more likely, there would be a massive blast in the panic room, probably killing the two girls but at least burning them both severely.
The first thing the intruders do is drill every window and exterior door shut with drywall screws. So, when the police arrive, Meg could not have opened the front door without undrilling it, and consequently, she would not have been able to convince the two officers that there wasn't any trouble on the premises.