Continuity mistake: When Pierce first begins to interrogate Caliban in the safe house in Mexico, a large portion of Caliban's albino makeup is smudged below his nose, revealing the actor's natural skin in his first close-up of the scene; after switching to a close-up of Pierce, then back to Caliban, the smudge has been fixed.
Continuity mistake: When Logan shoots Dr Rice at the start of the final fight, the shot changes to Logan and shows him firing a gun using his right hand. The shot changes to Pierce being shot, then to a wide shot showing all three men. The gun is now suddenly in Logan's left hand.
Continuity mistake: Before crashing the limo into the fence, there are two bullet holes in the rear windscreen. Afterwards, there are five. Then from an inside shot as they start backing up, there are only two again.
Continuity mistake: When Pierce is in the limousine, he pulls out a business card, and holds it out to Logan, who doesn't take it. In one shot, Pierce holds it with the writing facing himself, but in the next shot, it's upside down with the writing facing Logan, and you look closely, it only has print on one side.
Continuity mistake: Logan tries to give the Professor an injection, who pushes him away and falls over. As he falls back his left sleeve is still rolled up - the shot cuts and it's instantly right down to his wrist.
Continuity mistake: After Logan leaves the clinic and is walking with Laura on the street, just before they get in the truck the sun changes between shots.
Continuity mistake: After Pierce hooks Laura in the chest, she got some blood on the blouse and a hole, later in the convenience store she has the blood on it but the hole is gone.
Continuity mistake: In the opening scenes the gang thieves are working on his car with air tools, which require a compressor and air line. When Logan gets out of his car the thieves are using tire irons instead. (01:07:00 - 01:37:00)
Answer: Dr. Rice tells Logan the mutants have been wiped out due to a drug in the food and water supply that suppresses mutations, thus no new mutants had been born in 25 years. In the film series, it's indicated mutant powers usually come out during puberty, so parents don't know their children are mutants until around 12 or 13. So it took over a decade to realise no new mutants had been born. However, the government had been breeding mutants for weapons, which is where the mutant children come from in the Logan film. Furthermore, it is implied the "Westchester Incident" was an uncontrolled seizure of Charles Xavier that resulted in the death of many of the mutant students.
Bishop73