During the courtroom scene, Christian's ex boss explains that she last saw him on December 17th, which the lawyer points out as being the day after the murders, the next witness then states that he last saw him on December 19th, the lawyer says that this is two days after the murder, which would mean the murder took place on the 17th.
As Mike Finkel sits down to read the 'Wrong Turns' sent to him by Longo, Mike first turns the pages one by placing the 'read' page face up. Further, as he's reading more pages, the 'read' pages are placed face down. This switches back and forth continues throughout.
When Mike is reading the "Wrong Turns" letter from Chris for the first time, he turns the pages over and puts them to the right and it's visible that the back of the paper is empty. However, after the camera zooms to Mike's face and then back to the letter, the pages on the right have writings on them.
When Pat Frato calls Michael Finkle to get his side of the story, he tell's him that Christian Longo was captured in Cancun, Mexico. This is in part true, he was captured in Tulum, about 40 miles south of Cancun, however, when we first see Longo in the movie, talking to the German girl, they are in a church in downtown Mexico City. All Mexico scenes happen around Santo Domingo plaza, a few blocks from Mexico City's main square. Mexico City and Cancun are about 800 miles apart.
Michael Finkel's news story on child slavery was set in Mali, but the language spoken by those characters is Ibo, which is spoken in Nigeria, not Mali. The translator's name was Ibrahim, which is a Muslim name; he could not have been Ibo, because Ibos are only in Nigeria and are 99% Christian.
Christian and his wife were Jehova's Witnesses, yet in the teddy bear story, he tells Mike of not being able to give his children gifts for their birthdays, which is why he "passes down" the bear. Jehovah's Witnesses do not believe in celebrating birthdays, or other holidays, with gifts or otherwise.
When Mike Finkel is returning home after losing his job at the times, he is seated on a wide body Airbus aircraft, either an A330 or A340. The captain announces they will be landing shortly in Bozeman, MT. No airline has ever served Bozeman with a widebody Airbus aircraft.
While Mike is reading the letter from Christian, where it's mentioned he was raised as a Jehovah's Witness there was crosses depicted in his notes. This is a factual mistake because crosses are not used in the worship of Jehovah's witnesses and would not be seen in they're place of worship.
When Mike Finkel receives a call from Pat Frato to ask him about the Christian Longo story and makes him aware of Longo using his name when apprehended, Finkel googles his own name and the search results shown include one from gawker.com saying "· NYT journalist Michael Finkel, who was fired last year for fabricating a story, found out while he was contemplating suicide that Christian Longo (who was wanted in Mexico for murdering his family) was using his name as an alias because he liked Finkel's writing". This gawker.com post goes on to say "...HarperCollins is paying $300,000 for Finkel's story, including exclusive interviews with Longo"