When Cosmo said something about a team of superheroes and closing a portal to another dimension, he was referencing to The Avengers from Marvel.
The title is a reference to Ghostbusters.
The suffix "-inator" may resemble to Dr. Heinz Doofenshmirtz and reference to the show, "Phineas and Ferb".
After Wanda takes Cosmo's wand, it occasionally disappears or reappears in her hand.
In the episode, "Apartnership!". Timmy's parents have their anniversary when it's Cosmo and Wanda's anniversary. In "Birthday Bashed!", they have their anniversary when Timmy has his birthday. But in this episode, they have their anniversary and there's not a single hint if it's Timmy's birthday or Cosmo and Wanda's anniversary.
When Timmy and the fairies are stuck in the cage and Timmy is telling Sparky to get the wands out of the vacuum cleaner, he appears to be able to walk between the bars of the cage, but does not try to escape. Also Sparky only gets wands, no rattle.
In fact throughout most of the series, characters can fit their whole head between the bars of cages, but yet they never try to escape. And, like a cat, because their heads are the biggest parts of their bodies the way they are animated, if they can fit their heads through, they can fit their bodies through.
There are many times when Timmy should have seen the machine.
It's possible the sheer volume of Timmy's wishing mandated the installing of it in between episodes.
Couldn't Sparky have wished Timmy and is fairies out of the cage?
When Cosmo talks about fairies making bad names, he gave "We called our kid Poof" as an example. But in Fairly Odd Baby, the one who gave Poof's name is Timmy who is not a fairy at all.
Wanda said they can't make any more wishes or it will blow up the whole house, but they made a wish and nothing happened.