The earlier scenes are funny because they're like
"Hey, we've been trying for a month to break all known laws of physics and go infinitely fast, and we finally did it."
"Gee, that's great, good job everybody."
They're all pleased with themselves, but...like the way they would be if they created a more efficient duty roster or something.
They way Paris describes being everywhere in the Universe and once, and then the shuttle has the data collected on its computer is a massive failure of imagination/basic reasoning that is as stupid as anything else in the episode, if no moreso.
And WHY did they leave the babies behind??? That seems like several different kinds of wrong to me.
Some good stuff from Memory Alpha:
Supervising producer Brannon Braga later commented, "I wrote the episode, or at least the teleplay [....] And... it had some good intentions behind it. It had a good premise, breaking the warp ten barrier. I don't know where this whole 'de-evolving into a lizard' thing came from [....] I think I was trying to make a statement about evolution not necessarily being evolving toward higher organisms, that evolution may also be a de-evolution. You know, we kind of take it for granted that evolution means bigger brains, more technology, you know, more refined civilization. When in fact, for all we know, we're evolving back toward a more primordial state. Ultimately, who can predict?" (VOY Season 2 DVD easter egg) In a 2011 interview, Braga stated, "I was trying something [....] It was my homage, I guess, to David Cronenberg's The Fly." 
Paris actor Robert Duncan McNeill was bewildered by the episode's first draft script. "When I read the first draft," he said, "I couldn't get it. I thought they took on much more than could be handled in one episode." (The Official Star Trek: Voyager Magazine, issue #11) He also remarked, "When I first read that script, I couldn't believe they were going to shoot it." (Cinefantastique, Vol. 28, Vol. 4/5, p. 94)
Robert Duncan McNeill helped refine the episode's conclusion. "I helped them rewrite the episode's final scene. I did not feel the original story ended very well. I was pleased because I got to have some input into how to resolve the story." (The Official Star Trek: Voyager Magazine, issue #11)
In fact, Brannon Braga thoroughly edited the script during the rewrite process. He remarked, "It's very much a classic Star Trek story, but in the rewrite process I took out the explanation, the idea behind the ending, that we evolve into these little lizards because maybe evolution is not always progressive. Maybe it's a cycle where we revert to something more rudimentary. That whole conversation was taken out for various reasons, and that was a disaster because without it the episode doesn't even have a point. I think it suffered greatly. I got the note that it wasn't necessary, but in fact it really had a lot to do with what the episode was about. Big mistake taking it out." (Captains' Logs Supplemental - The Unauthorized Guide to the New Trek Voyages) Later, Braga complained, "Unfortunately, none of [the evolutionary theorizing] came across in the episode. And all we were left with were some lizard... things crawling around in the mud. So, it was not my shining moment." (VOY Season 2 DVD "easter egg") In 2011, he named this episode as the one installment from the entirety of Voyager that he would "just as soon forget" and remarked, "That's a real low point [....] It really backfired on me. It was poorly executed by me." 
This episode's final script draft was submitted on 31 October 1995. 
Regarding the hypothetical concept of infinite velocity, science consultant André Bormanis remarked, "It's fun to invoke paradox when you're talking about something as bizarre and as hypothetical as warp drive. And so, that idea become the basis for a story where Tom Paris thought that he had figured out a way to sort of 'crash' the warp 10 barrier and was eager to try to implement this, and see if he could actually achieve warp 10 flight [....] Unfortunately, when Paris did achieve warp 10 flight, it had all sorts of unintended consequences and, physiologically, he started mutating and turning into something bizarre and strange. And the story went off in a really unconventional and kind of horror movie direction, after he had broken the warp 10 barrier. But all of that is basically the consequence of taking one of Gene's original ideas, from the beginning of Next Generation, and extrapolating and playing with it and finding an interesting way to use that as the springboard for a fun science fiction story that we can tell with our crew." (Real Science With Andre Bormanis, VOY Season 2 DVD special features)
André Bormanis believed the first part of the episode, involving Paris breaking the warp 10 barrier, had similarities to a certain historical event. "It was a little bit of an analogue to breaking the sound barrier," Bormanis commented, "the famous story about Chuck Yeager and the X-1 in 1947, finally breaking the sound barrier." (Real Science With Andre Bormanis, VOY Season 2 DVD special features)
In the shooting script of this episode, the eponymous shuttlecraft that breaks the warp 10 barrier is named the Drake. However, a shuttlecraft of that same name is destroyed in the earlier second season episode "Non Sequitur". The eventual name of the shuttlecraft here was the Cochrane, named after Zefram Cochrane. (Star Trek: Voyager Companion)
Robert Duncan McNeill was generally puzzled by this episode, so he tried to rationalize it for himself. "When you try to tell the story–he breaks warp ten, starts shedding skin, he kidnaps the captain and then he becomes one with the universe, [he and Janeway] are salamanders, and have a baby–it sounds ridiculous," McNeill remarked. "What is this about? Before you can even start to tell the story you have to find the moral. What is the simplest point of this episode? Once you can say that in a sentence then that is what the episode is about. To me [...] the whole warp ten [challenge] and salamanders and all of that frosting was about Paris trying to find some sort of salvation outside himself and ultimately realizing that he had to find his own self worth from within. Here is somebody who thinks he's got to break warp ten and prove to everybody, his father and himself that he can do this outside thing, but ultimately your happiness comes from within." (Cinefantastique, Vol. 28, Vol. 4/5, p. 94) In the end, McNeill still thought the episode was very strange. "That was a bizarre show," he exclaimed. "It really was." (The Official Star Trek: Voyager Magazine, issue #11)
On the other hand, Robert Duncan McNeill also enjoyed scenes that were important for his character, especially one that essentially epitomizes his interpretation of the plot. He enthused, "I like a few scenes that I thought were important for Paris. I like the one where I explain to Janeway how I need to prove myself by breaking the warp speed barrier." (The Official Star Trek: Voyager Magazine, issue #11)
Despite his mixed feelings about the story, Robert Duncan McNeill extremely liked appearing in this installment. He described it as "[an] episode I really enjoyed" and, moments later, said, "I loved getting the opportunity to chew the scenery a little bit." (Star Trek Monthly issue 37, p. 44)