When we last saw Happy Peppy Gary and Betty, they were being taken away in Mark Chang's spaceship in Totally Spaced Out. There is no explanation for how they got back in this episode, other than presumably that Timmy wished them back and unwished their memories of the event to prevent any problems.
Pops the Adult, the old man at Camp Learn-a-Torium says that he was dropped off there 60 years ago and his parents never picked him up, but Flappy Bob is only thirty seven and did not create the Learnatorium until after college. Also it's never explained why Betty and Gary force Pops to remain at the Learnatorium as he's over eighteen and no longer their responsibility.
When Timmy first finds the place in the license plate maker where you stick letters in, there were 7 slots, but later when we see him spelling "I wish I was ten", there are 12 slots, enough to fill in that sentence, without the spaces
Happy Peppy Gary and Betty punished Baby Timmy because they were nearly eaten by gators, it is unknown how they knew that Timmy (an infant) was the one responsible for them ending up in the everglades. Timmy could not have said it out loud clearly due to being a baby and there is no way they could have seen what the message with the blocks was since they were too far to read what Timmy was saying with the blocks.