Ok, Tuvix, lets get started *rubs hands together*
1) The imaging scanners on the transporters were malfunctioning, which sounds to me like a good reason not to use them, but hey Janeway doesn't really care about her crew's safety so we can ignore the decision to use them. The question remains, why were there only one set of imaging scanners, when the transporters have multiple redundant systems, precisely to avoid this sort of accident. Even if all the transporters run through a single set of imaging scanners, there are plenty of shuttles that have working imaging scanners (they don't say they're not working, so we can presume that they are). Though this is an old complaint against Trek writers, the inability to use the shuttle or cargo transporters, it's still irritating, though strangely TOS usually had an actual reason for transporters as a whole to be non-functional, such as interference or something, whereas more modern incarnations just sort of say "they don't work, that is all".
2) If Tuvok and Neelix got fused into a single life form, that's not really any bigger than either of them, where did the rest of them go? And where did all the bits of them come from when Tuvix was ripped apart?
3) the main premise is laughably stupid, that a flower could cause to people to fuse into a single, living organism, instead of a pile of biomatter on the transporter pad. See I can buy that the flower might cause something, it's pretty stupid, but not overly so, but the fact that there isn't a mound of flesh and bone that rematerializes on the transporter pad crosses the line, it's completely over the top. Of course the rest of the episode doesn't really dwell on it too much, there's some stuff from the Doctor about how he'll reverse it, but it's primarily about how Tuvix adjusts to being a new member of the crew, and how the crew essentially rejects him.
4) Janeway makes an end of life decision for Tuvix, despite having no legal authority to do so; Tuvix is a living sentient being, he has every right to choose whether to undergo the procedure, and Janeway doesn't have the right to overrule him. Essentially, the moment Tuvok and Neelix were dematerialized, they were dead, there's no reason to risk this new lifeform, which is frankly a slight improvement on both characters, on the chance of bringing two dead crew members back from the grave, and risk loosing all three.
I will say this, the performance of Tom Wright (Tuvix) is what makes this episode, if they'd cast a weaker actor the whole thing would have fallen through, but he gives such a performance that you sort of forget all the idiotic and borderline psychotic things that happen in the episode, and focus instead on the struggles and death of Tuvix.
Plus the episode had Neelix die for a bit, in possibly the worst way (ripped apart into nothingness), which again, amuses me greatly (you seem to have a knack for choosing episodes where Neelix gets what's coming to him, bravo).
I would recommend watching the review of Tuvix by SFDebris, but it's not online at the moment, he's in the middle of re-mastering all his videos because of a youtube stuff up. Chuck is much better at this than I am, and his analyses are far more in depth. Don't let the crude humor fool you into thinking it's just Voyager bashing. In the meantime I would recommend watching his review on
Caretaker, where he explains the high hopes he had for Voyager back in 1994, and what quickly drove him (and a large chunk of the audience) away.