Factual error: After the intruders flood the panic room with propane, Jody Foster's character gets a lighter and ignites the propane causing it to burn along the ceiling. This would be impossible as propane is heavier than air and would sink to the floor rather than rise up to the ceiling. Lighting a flame in that room should have caused anyone in the room and on the floor to be engulfed in flames almost instantly.
Other mistake: Near the end of the movie Dwight Yoakam is holding Jodie Foster's daughter captive as he tries to exit the house. Jodie Foster sneaks up behind him with a sledgehammer and swings it at his head. He turns to face her and the metal end of the hammer catches him firmly in his temple, knocking him down a flight of stairs. A few minutes later he comes up the stairs and tackles Jodie Foster to the ground, seemingly unhurt by the impact of the sledgehammer.
Character mistake: The mother tells the daughter to keep warm and drink water. In fact that would lower the blood sugar faster. This method is used for high blood sugar to lower it back to normal.
Continuity mistake: During the first meal in the new house, the level of Coke in the daughter's glass keeps changing as the camera cuts between her and her mother. The Coke can revolves as well. Sometimes the Coke-logo is visible, at other times the list of ingredients is facing the audience.
Audio problem: When Jodie Foster first hears a ring at the front door, Steven says, "The police." and Jodie says, "You called the police?" He responds with, "Of course I did. You scared the s*** out of me." When he says, "You scared the s*** out of me.", his mouth movement does not match what we hear.
Factual error: When Kristen Stewart is flashing SOS in morse code through the hole her mother asks "where did you learn that" she then replies "Titanic." In the movie 'Titanic' they correctly used the proper distress signal of the time which was actually CQD (CQ is Code for 'All Stations' and suffixed by 'D' for distress). CQD in Morse code is -.-. -. - -.
Continuity mistake: When Meg and Sarah are inspecting the house in the beginning of the film, Sarah's bag has pawprints on it in the first shot. In the second shot the pawprints change to faces.
Continuity mistake: The girl is inside the room with Forrest Whitaker and the other guy, about the time Whitaker picks up the red thing with the needle, watch the loose hair on the right side of her head, close to her ear: It keeps moving up, down, sometimes is wetter, sometimes dryer. And the girl barely moves.
Factual error: When the burglars use the crowbar to break through the roof hatch, the security system display changes from "System Armed" to "Zone 19 Disabled" which can only occur when the zone is disabled by the user. Additionally, the alarm should have sounded immediately when the sensor on the hatch was broken. If the circuit had already been disabled then the security system would not have reacted by saying "Zone 19 Disabled."
Continuity mistake: When Junior is shot in the head, the original bullet wound is almost exactly between the eyes, but when you see him lying on the floor, the bullet wound is over his right eye.
Continuity mistake: It's raining heavily all night, but when Burnham goes up on the roof to look for a way in, you can no longer hear the rain falling on the window. Later on, we see the rain falling heavily again.
Suggested correction: Rain does that all the time. Starts and stops, drizzles and pours. This is not a mistake, but rather how Mother Nature works.
Continuity mistake: Junior's right arm is set on fire, but afterwards, he is stretching his left arm in pain.
Continuity mistake: When Sarah lays down in bed, the towel is still around her head. But a second later, the towel has gone and her hair is dry and brushed.
Other mistake: Raoul told Junior he wanted ⅓ of whatever's in the panic room, but Junior told Burnham only the two of them (Junior and Burnham) knew the money was in there.
Suggested correction: Like you said, Raoul stated he wanted 1/3rd of *whatever* is in that room. He doesn't know what's in there, but he would assume it would be valuable.
Other mistake: According to the cops at the door, Meg's husband revealed to them that Meg said "There are three" on the phone before the line was cut off. However, earlier in the film during the call, Meg said "There are three men..." and then the line was cut by Burnham. The husband would have heard the word "men" as well to give to the cops.
Suggested correction: Steven (the husband) was just woken up in the middle of the night to a frantic phone call from his wife. Very possible he did not hear, or simply did not recall hearing that one word.