According to the first title card, Frasier graduated high school in 1968. According to other episodes, the year of his birth was 1952, which makes graduation in 1968 unlikely at best.
(At 00:01:13) Niles puts the lid back on the sugar dispenser just as Frasier sits down. The camera then cuts to Niles and the lid is back in his hands and he is shaking it off into his coffee.
When Roz sits at her Cafe Nervosa table, the lid of her sugar jar is badly skewed. In the next shot, it is screwed on straight.
Martin tells Niles that he bought the wrong dog food and needs to return it, but when Niles picks up a can to read it, Martin says that it's Eddie's favorite kind.
In Nervosa there are two girls sitting at the window, next camera angle they are gone, in next scene with Frasier and Niles they are back, then they vanish again. They then reappear and get up put their coats on and leave, then next scene they are back as if nothing happened, then they vanish again to reappear again. All this happens in the two minute 30 second cafe scene.
Frasier mentions that the stove is electric, but it's clearly gas.
When Niles finds Frasier with his head in the oven, he says not to worry "it's electric".
But the burners for the range are gas. And since it's on the same island as the oven.
It seems unlikely one would be gas and one electric.
The two girls in Cafe Nervosa who are laughing at Niles get up to leave shortly after Frasier sits down. However, a few shots later, they are comfortably sitting back in their seats, reading from books. They do not actually leave. The mother just gets up and walks away from the table (presumably to use the restroom), then returns a few moments later and sits back down.
When Frasier shows off his belt to Mr. Rugley, he says, "I cut through the park on the way over here and it caught the eye of many a young lady." But then during his interview, Frasier has his car towed from Mr. Rugley's parking space. If he drove there, he obviously couldn't have walked through the park as well.
Frasier bangs his head after Niles shouts at him when he finds him with head in the oven.
Frasier gets saying the oven is electric. But the range just above it is gas. It would be quite
unusual to mix energy sources for this two appliances, especially when they are so close together.
Frasier says that Diane abandoned him at the altar 10 years earlier; it happened 13 years earlier.