Meet the Robinsons/WMG

Lewis' mother was a teenager.
She had a rather conservative father, and was not supposed to be seeing any boy at all, let alone sleeping with her boyfriend. But she got unlucky. Although she managed to Hide Her Pregnancy (can't have been easy--she looked pretty slender), she and her boyfriend knew they had to do something with the baby. They did research into safe haven laws, found out that the orphanage was an appropriate place, and left him there. She was just young enough to think the whole Door Step Baby scenario--in the rain--might fit, and she couldn't risk being noticed by someone who might try to talk with her father.


 * Maybe she was a single mother too poor to take care of the baby and/or she lived in terrible conditions and wanted a better future for the baby. Or she was a single mother who had a terminal condition and knew no one to care for the baby and didn't want to die with the baby in her possession. Or she was a married mother who lost her husband and didn't want her child to be fatherless but she couldn't find a suitable mate. Or in a variation of the death thing maybe she was in danger, like the Mafia or someone was trying to get her and they already got her husband and of course she didn't want the baby to be in danger or maybe even worst the baby be left alone so the only thing she had to do was leave the child at the orphanage. There's so many other circumstances that aren't as "controversial" or fit for a teen movie or some Lifetime movie where the bad guys are made to look like the the good guy. Remember, this is a darn kids movie...

Lucille was literally baking cookies in the disco hall.
One of Cornelius' many inventions is a supermodern kitchen connected digitally to a dance floor. People can command robotic implements to grab two cups of flour, a spoon of baking powder, bake for two hours at 200 degrees, etc, by doing various moves, like an extreme version of Dance Dance Revolution. Over time, various dance moves started becoming associated with the respective recipes they were used for. So "baking cookies" wasn't just slang, it was literally the cookie baking dance!
 * So Bowler Hat Guy stole that idea and sold it as the Playstation Move?

Frankie the talking frog has a good friend named Jeremiah.
He is a bullfrog, and nobody understands a single word he says, but always had some mighty fine wine.
 * Somewhat confirmed. "So I turn to the bullfrog, and ya know what I says? I says 'Hey, not with my umbrella you don't.'"

A prankster from the Robinson family is responsible for Michigan J. Frog.
One of Franny's singing frogs + time machine + strict instructions on when to sing and when to act just like a regular frog = Generations of Hilarity Ensues. At least from the prankster's (possibly Wilbur) point of view.

There are no temporal paradoxes.
The original timeline was created without time travel. When time travel is used and Lewis sees his future inventions, the timeline falls back on itself.

The Time Continuum Task Force, or something like it, becomes a reality sometime after the events of the film (in the future).
Cornelius' time machines are commercialized, but strict regulations must be placed on their use due to the possibility of abuse and/or inadvertently altering the timeline for the worse (as we know from the movie, changing the past with time travel is an easy thing). The government of the future sets up a real Time Police department. Wilbur actually ends up joining them, making his initial self-introduction to Lewis partly true From a Certain Point of View.
 * Also, shortly after the movie, as one of the first time travellers (and now fully aware of how dangerous changing time can be), Wilbur gets a job there.

The movie is set in the same universe as Power Rangers.
And strengthening the above theory, the Time Continuum Task Force could be the "extended" name of the Time Force Police.

There is more than one Tom Selleck.
Specifically, there is a Tom Selleck in the future who resembles Lewis. He was the one Wilbur was referring to, assuming Lewis would know who he was.


 * Maybe Wilbur really meant his father sounds like Tom Selleck because Lewis asked what he looked like and of course Wilbur couldn't say "You!", so he told a lie with some truth to it that fit the moment and said he looks like Tom Selleck. And maybe Wilbur learned about Tom Selleck in History class, who knows, maybe in the future they'll have a "Hollywood History" class in presumably Middle School, if that type of school still exists.
 * Actually, this troper just found out that that bit is explained in the DVD commentary. I can't write it word for word (my memory's like a goldfish's), so if you have the DVD, listen to the commentary and find out why Wilbur mentioned Tom Selleck. And if you don't have it...buy it.

Lewis's mother was a "lady of the evening"
My husband and I both just watched this for the second or third time, and noticed his mom is dropping him off in red high heels. Or they look like red high heels. Dropping a newborn off in the middle of the night, completely covered up, and extremely nervous, plus the inappropiate shoeware for a watery ninja baby drop....