Why does Tiny the Tyrannosaurus fall into line quickly after the mini-Doris is knocked off him, and why does the Robinson estate have an octopus butler and a dog that wears glasses? Apparently, animals on the grounds tame down quickly and get Amplified Animal Aptitude. And why would Lewis invent that? To give Franny her dream of singing frogs.
Why is Franny so very moved when her son tells her that his new friend Lewis is an orphan? Because she's married to one, and personally knows from his example that it's a rough way to start out in life.
This also explains (explains; not justifies) Wilbur's casualness in relating Lewis being an orphan. Growing up with a dad who was one has made him think of being an orphan as being no big deal since it worked out well for his dad. He just doesn't understand.
Also, the future seems to be significantly Sugar Bowl-esque, so child homelessness must be very rare in the future. Especially considering Lewis had to go through being an orphan, is very kind, and can now impact the world to the point where he can prevent other children from becoming orphans as well, or at least make sure orphanages weren't the underfunded dead-end they were when he was there.
The ending is far happier for Goob/Bowler hat guy than you might think. Not only does he get adopted and have his future changed for the better, he's adopted by the Harringtons. Mr. Harrington earlier showed an interest in baseball, very much like his new adopted son Mike. What's more, now "Goob" doesn't have his embarrassing nickname anymore. As of this point, he is no longer Mike "Yagoobian", but rather Mike Harrington.
Wilbur Robinson's appearance resembles Franny more than Cornelius because if he looked like Lewis and went back into the past to prevent the Bowler Hat Guy from ruining his dad's future, the fact that he resembles Lewis would have been a dead giveaway to Lewis that something odd is going on!
Genetically, it makes sense that Wilbur would have some of his more obvious traits from Franny. Brown eyes are dominant over blue, and dark hair tends to be dominant over light hair. Franny and her brothers are Italian-American, so it's likely they are all homozygous dominant (meaning they possess two dominant genes and thus can't pass along recessive genes) for hair and eye color. But Wilbur does appear to have his dad's jaw and ears.
Franny tells Lewis that she is "always right", and Cornelius advises him to "go with it". Later, when Lewis meets the younger Franny, he gains her affection by telling her that she's right about her hobby of teaching frogs music. The older Lewis/Cornelius and Franny probably remembered that moment.
The Bowler Hat Guy's identity is revealed when he tells Goob to hold on to his grudges. Anyone who's familiar with time travel cliches knows he's trying to make sure he still exists in the timeline!
Wilbur claims his dad looks like Tom Selleck. Maybe he's aware that he sounds like him, and that's what first came to his mind when Lewis asked.
Something that when it first appears it seems to be a headscratcher, but watching it the second time explains it. Wilbur doesn't look like a kid from the future and Lewis has some trouble believing him. When they go to the future, Wilbur puts a hat on Louis so no one will recognize him as a kid from the past. Why would his family think that he looks like a kid from the past if people in the past couldn't recognize a kid from the future? They wouldn't recognize any kid from the past, only Cornelius because of his Anime Hair that he still has.
Apparently in the Bad Future, Doris did something to Goob after taking over. After a little while, the brain machine POWERS OFF like static. Who knows if the brain was just attached to the machine after Doris KILLED Goob?
Milder example, along the lines of Fridge Cringe. When Franny asks Wilbur "What did he mean 'if' he had a family?", Wilbur is totally casual when he replies that Lewis is an orphan. He probably should be glad Lewis didn't hear him.
Subtle, but no one seems to see anything wrong with Lewis calling "North Montana", "Canada", despite his saying that he supposedly lives there. The most likely reason for this is that a lot of the people there didn't like the union/annexation and insisted on calling it Canada. Hence, the lack of follow-up on that was because it was still a politically touchy subject.
There was a deleted scene in which Lewis takes Bowler Hat Guy back to the past with him to give him the chance to wake a younger Goob up in time to catch the ball, an offer he accepts with heartfelt thanks as he disappears from existence. Compare that to what actually happened in the movie, in which a nervous Bowler Hat Guy disappears leaving his trademark list behind, the final item being a question mark. Lewis later goes back to the past alone, and wakes Goob up himself, thusly flinging Bowler Hat Guy headlong into nonexistence. Keep Moving Forward!
Actually he's probably happy somewhere, maybe playing baseball. He didn't erase him from existence unless Goob died between then and then.
To explain, the Bowler Hat Guy was necessarily erased in that he no longer exists. Because Goob woke up, caught the ball, and won the game, chances are that his life is going to go into a different direction. The Bowler Hat Guy still exists, only he's not the Bowler Hat Guy, he's just an adult Goob who'll have probably had a better life.
Wilbur had a time machine. What was stopping him from just going back in time to the moment that he left the garage door open and closing it?
I'd like to think it was because Goob's future needed to be saved and fate made sure it was.
Alternatively, Bowler Hat Guy isn't the only person who doesn't think things through.
Could have been a paradox. If he went back in time to close the door, why would he need to go back in time in the new timeline?
Or ripple immunity. Even if he closes the door now, Bowler Hat Guy has already traveled backward in time, so he still needs to undo any damage he does.
When Wilbur is roped into helping young Franny into gathering her frogs up, he is obviously annoyed with her, even pulling a Not Now, Kiddo...or rathertrying to. However when we see Wilbur next to the adult Franny, it becomes clear that he lookslike a male version of her. Why did he not realize that the girl he was helping looked a lot like his mom?...to say nothing of her having a bunch of frogs and the fact that he was there in the first place to find the younger version of his dad.
The same reason you have no idea where (insert item here) is until seeing it for the third time when looking, and change blindness. The former is because you forget certain things when you do them by muscle memory, and the latter is because if it's similar enough to what you remember, your brain ignores it. His brain was on "power-saver" and he was focused on the task "Find Dad".
If Doris had succeeded in her plan to sabotage Lewis's invention at the science fair, he might have given up being an inventor. Which means that he would have never invented her. She was inadvertently arranging her own non-existence.
It's best to hold up the MST3K Mantra high when trying to piece out the time travel logic in this movie.