Another confusing point is the ages of the various characters from the older generations. James, Lily, Sirius, Lupin, & Snape were all in the same class in school. [We see this in many places, the most obvious in Snape’s Worst Memory] Snape was also in school with Avery. . So Avery is minimum of two years older than James, because he was in school at the same time, and this conversation takes place in James’ fifth year (OWLs).
However, we see that Voldemort was in school was Avery [see Slughorns memory of Horcruxes, Avery is present, with Rodolphus Lestrange]. Meaning that Tom Riddle was in school with Harry’s parents, in the same class or within two above.
Which is strange, because we have no mention of that. Not from Hagrid, not from any teachers, not from Madam Rosmerta [book 3].
Worse still, Dumbledore says “Very few people know that Lord Voldemort was once called Tom Riddle. I taught him myself, fifty years ago, at Hogwarts”. That doesn’t make sense at all, because Harry’s parents were married young and were just starting off. (Can’t be bothered proving everything from quotes, but if you got any problems you can just ask!)
When Dumbledore is going through the Pensieve with Harry, he shows Voldemort working in Knockturn Alley, and then a disappearance of ten years “which we can only guess what he was doing”. So Voldemort didn’t rise to power (his Death Eaters were still a secret at that moment, see further in that chapter) for at least ten years after he left Hogwarts.
Even worse is that Arthur and Molly apparently got married when Voldemort was rising to power (“People eloping left right and centre”), meaning that they would have to be younger than Voldemort, and have been in school with James and Lily.
Another point was that Riddle left the school with Dippet in control; Lupin announces that Dumbledore became Headmaster when he was in school. And Dumbledore himself (in both Riddle’s memory and his own) was much, much, younger, and merely a Transfiguration teacher.
(The only real problem is Avery being in school with both Lily & Tom Riddle. If you ignore the instance of Avery being with Lily, and put him with Tom Riddle, everything makes more sense.)