
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: 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.
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.
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