Reuben's special skill has always been making sandwiches... until Leroy & Stitch, when he successfully repairs a space shipwreck and gets it off the ground. Making a sandwich or (any other snacks) is sometimes called fixing a sandwich, etc.
In the movie, Stitch is sentenced to exile on an asteroid. In "The Asteroid", Stitch and co. travel to an asteroid to destroy it, only to find it inhabited by a lone alien. Now we have an idea about how he got there.
In "Mr. Stenchy", it's shown that Stitch lacks a Good Angelshoulder conscious, instead of having two Bad Angels. Since he wasn't designed to have one, Lilo became his voice of reason.
The Four Crossover Episodes actually suggest good explanations for the series' little inconsistencies that wouldn't be possible to be explained otherwise:
The Night Marchers from "Belle" seem a little out of place in a Sci-fi series since they are clearly ghosts, but if you take into account Jake Long lives in the same universe, they could just be magical beings that are on the run.
Technology like the 'automatic dehydrator' from "627" seem kinda odd... until you realize that they share the same world of Kim Possible, where Weather Machines are sold like cars. Who's to say that this isn't the same manufacturer or a similar fashion?
In fact, this could even explain Spinelli's father is revealed to be a secret agent in-universe, or whom Cobra works for now. Maybe both are agents of Global Justice from Kim Possible?
And it also justifies the existence of Warmonga and her people (along with the Area 51 aliens seen in Rufus vs. Commodore Puddles) in Kim Possible. It's the same universe of Lilo and Stitch, where extra-terrestrial civilizations are undoubtedly real.
Jumba's increased use of broken English in the series compared to the original film seems like Flanderization at first. Then I remembered that many of the human characters are also speaking pidgin English since it's spoken widely in Hawaii in real life. Evidently, Jumba has been on Earth long enough for local styles of speech to influence how he talks.
Mertle's Flanderization (becoming an even bigger Jerkass than she was in the first one, outright bullying her, etc.) seem rather odd, but then two things happen around the time the series ends. In Stitch Has a Glitch, which is an interquel set between Lilo & Stitch and Stitch! The Movie, Mertle mentions her father. Then Leroy & Stitch reveals that her dad "ran away". These two combined paint a more tragic explanation for her change in behavior: sometime between Stitch Has a Glitch and Stitch! The Movie, her parents got divorced. Confused and upset, she took her anger out on Lilo, causing her to become even more of a Jerkass than she was in the original film.
Lilo's seeming to abandon experiments in some episodes might seem like it's really out-of-character for her to do so. Then one might remember that in the original film, she spends so much time with Stitch trying to help him become a better person only for nothing to improve for her and him (or so it seemed before the climax hit), she runs out of patience with him, telling him to go away after he accidentally destroys her house in his fight with Jumba. It's pretty much the same ordeal in those episodes of The Series; no matter how hard she tries, those episodes' experiments were not getting any better. She ran out of patience during those times and decided it was not worth trying to help them anymore. (In fact, this was more obvious in some episodes than in others, such as in "Heckler" when that rude experiment insulted her and the "'ohana" and "one true place" phrases she loves.) Not to mention, she is a kid; children often don't have the best patience in the world.