Character mistake: A TV news announcer describes Alan Shepard's first manned launch into space as him being lifted to "an altitude of 116 miles per hour." That's not an altitude, that's a speed. It should have just been "116 miles."
Factual error: During the 31st year of the Avalon's voyage, the ship passes close to the star Arcturus, which is about 37 light years from Earth. Later in the movie, it was stated that the Avalon was moving at around 50% of the speed of light. The ship would not have reached Arcturus in the time allotted.
Continuity mistake: When the police are moving in to arrest Dzhokhar Tsarnaev, the shot shows an FBI SWAT officer grabbing him. But in the next cut, the officer changes to a Boston Police Officer while changing back to a FBI Officer in the following shot.
Continuity mistake: When Ray Kroc first orders a meal from McDonald's he is at the order window on the left. As soon as he walks away from the window he is at the right window.
Continuity mistake: While Katie Couric is interviewing Sully, the first shot shows her with a portfolio in her hand and she is not wearing a ring on her left hand. The camera goes to Sully, then back to Katie and suddenly there is a ring on her left hand.
Continuity mistake: When a bunch of guys are out back passing around a bottle of liquor, the amount of alcohol in the bottle increases at one point.
Character mistake: Civil rights lawyer says bring up the 1983 case. Should have been 1893 or 1883.
Continuity mistake: In the scene when Dorothy hands her bible to Desmond on the bus, he is seated on the passenger side. However, after the bus departs, he is suddenly seated on the opposite side. (00:26:45)
Factual error: Round gallon ice cream containers did not exist in the 60s.
Suggested correction: The container in the film is a quart and the brand Dreyer's had that style of container as early as 1928.
Factual error: The film shows cactus and agave plants in many scenes - those plants were imported from the Americas to Judea 1800 years after Jesus.
Plot hole: There's no way that Eddie and Nana left the flooded theater without getting a single drop of water on them. The water flooded up to the ceiling and there's no other way to exit besides the front doors, and Moon's secret exit, which also floods. They do not leave through either way.
Factual error: When Eakins returns to the house after he swears an oath to the union. You can see a thermostat on the wall behind him. (01:40:00)
Continuity mistake: Ben got his job. He has to see his wife though, and she passes him the divorce papers. The papers are in an envelope she slides across the table with the flap face down. It's face up in the reverse shot. (00:06:30)
Audio problem: In the beginning, you can hear the sounds of the jungle, including the laugh of a kookaburra. The problem is: The film is set in India and kookaburras are only in Australia, not India.
Character mistake: When Mike's wife is watching the news about the oil rig on fire, you can see the TV with part of the U.S. map on it and 'Mississippi' is misspelled as Missisippi. (01:09:10)
Factual error: The license plate of the car that takes the protagonist to the sanitarium is GR 36E46. That's not a valid Swiss plate: GR indicates the canton of Graubünden, but other than that it is supposed to have only digits and no letters.
Factual error: The villain performs his hit at the beginning of the movie by remotely changing the GPS destination of a cab, so they head to the wrong place and into an ambush. Assuming that neither the cabbie or Pope notice the change on screen, and that his sophisticated software silenced the voice announcement of the course being recalculated, and makes the new place also marked as the old one (it is after all a god-like movie software), the trick is done on on a London black cab, whose drivers are notorious for "The Knowledge", aka being required to learn the entire topografy of the city in one of the most demanding training courses in the world, and not using GPS. It'd be definitely unlikely for the cab driver to be totally unaware, to the point of Pope himself noticing first that they are at the wrong place.
Revealing mistake: When a contractor fires a grenade at an enemy technical, the truck visibly explodes and moves upwards before the (most likely) CGI projectile hits it. (01:02:00)
Factual error: When researching Christian Wolf in the IRS database, they state he made $75,000 and ran ZZZ Accounting. They then look up 3 other businesses with over a million dollars in income, said they were all partnerships and stated that Christian Wolf was managing partner. Given that partnerships are flow through entities for income tax purposes, all that income would flow through to individual returns, resulting in much more than $75,000 in income on Christian Wolf's tax return.
Other mistake: When Amy Adams leaves the spacecraft for the final time she is met by Jeremy Renner who throws a blanket around her shoulders. As he does so, the blanket gets caught on something out of view top-of-frame (presumably a boom mic) and he has to tug at it to free it. This was part of one long take in fading light and given the amount of background action going on it was presumably too difficult or time consuming to re-shoot. (01:32:55)