Miss Finster has a raspy voice because she smokes, or used to.
Spinelli's size changes as the series goes on. She's the shortest at times, but at the end of the series she's TJ's height. This is due to a growth spurt.
A lot of one time characters disappear without an explanation while some leave at the end of an episode. It's possible Geldman the Bully scared them away, like he did to the kid at the beginning of "Gus' Last Stand."
Ashley, Tyler, and Britney/Brittany are all very common names; it would make sense that there would be more than one in the school. The Parents' Night episode implies that the Ashleys' mothers are all friends so it could make sense they'd all give their kids the same names.
In "Speedy We Hardly Knew Ye", Miss Grotke knows full well that Speedy has died and is trying to use the 'meditation' excuse to buy some time for her to replace Speedy with a new hamster.
In a few episodes we do see Mikey's dad and he's a hippie. That could explain Mikey's love for poetry, he's either copying his dad or got turned onto it.
There's a background character named Phil (he's the one in the scout uniform, red curly hair, buckteeth) who is in a few episodes. He's part of the Woodchuck Scouts, which is meaningful for his character design considering he has buckteeth.
In the episode "The Challenge" at Fifth Street Elementary (Where Prickley's brother's the principal) he meet the gang's doppelgangers at the school. The episode after it is when Spinelli does ballet we meet some Ashleys doppelgangers named the Megans. Since we don't see them in the previous episode, it's safe to assume they attend Fifth Street.
Miss Finster's heart-to-heart with Spinelli in "That Sinking Feeling" comes after the events of "The Trial". Finster remembers Spinelli helping her cat out of the tree and wants to make her feel better when she sees her looking depressed.
Both Mikey and Randall have deeper voices as Kindergartners than they do as 4th Graders in older episodes. Obviously, it's because Recess: All Grown Down was made at the end of the series, after the voice actors' voices changed, but that still makes one wonder why they didn't have someone else fill in the role.
If Gus looks cool without his glasses, why doesn't he get contacts instead? He'd be able to see and people would like him.
Where I grew up, most parents didn't allow their children to wear contacts until they were around fourteen or fifteen.
If everyone got sick from eating the tacos in "The Omega Kids" why didn't they just cancel school?
I think they'd have to wait until the end of the day to see if any children who didn't get sick showed up. The gang showed up so school was back on.
In Recess: School's Out the school is closed for the summer, hence why Phillium Benedict uses it to perform his experiment on getting rid of recess. Where do kids who have summer school go?
Possibly the kids who had summer school went to a different school for that. There are some districts that just send all the summer school kids to one school.
They might not have summer school at all; my elementary school didn't.
Dr. Slicer, his treatment of his students and his Nazi-like behaviour raises few uncomfortable questions: 1) Considering his personality, cruelty and his methods what knows what could have happened if Slicer would have taken over Third Street School and remember that he made TJ (who always stands up to adults and rebels against their evil behaviour and students are always win because of him) afraid and unable to rebel, 2) What if he was the principal of the other schools and what could have happened in those schools, 3) Considering his Nazi-like behaviour, he may be worshipping Nazis and Hitler.
In The Movie, Benedict's plan to destroy Summer is bad enough from a kid's point of view, but then you look at it as an adult and realize that he was effectively trying to restart the Ice Age, which would almost certainly destroy civilization, if not humanity in general. All for the sake of test scores.