As far as I understand it, Tuvok and Tom Paris never got "demoted" in Season 1. It was probably a costume error. For example, Tuvok was being referred to as "Lieutenant" from the beginning. At some point during Season 1 this was appparently noticed by the production crew and Tuvok's and Paris's rank insignia were adjusted accordingly (Tuvok went from "Lieutnant Commander" to "Lieutenant" and Paris from full "Lieutenant" to "Lieutenant, junior grade").
In my opinion, this was a pretty silly (albeit minor) mistake and it's hard to understand why it took weeks for anyone to notice. But that's how it is. I think there's even a mid-Season 1 episode were either Tuvok's or Paris's rank insignia kept constantly switching throughout the episode.
As for the original question... yeah it was awkward that Harry never got a promotion. It's not like Voyager would have been overcrowded with senior officers if Harry had been made a Lt. j.g. As long as there's only one Captain, one Commander and not many Lieutenant Commanders around, I'm perfectly cool.
The latter TOS movies became a bit ridicilous in that respect... with the command crew consisting of several Captains and several Commanders. (Yeah, I know that's how it's done on bigger ships in today's U.S. Navy, but for Star Trek it was extremely unusual.) Realistically speaking, Kirk, Spock, Scotty, and Sulu should have commanded their own ships in TUC with Chekov being Kirk's XO and Uhura being Spock's XO or something along those lines.

But I guess that was hard to put into practice... can't have a movie with four separate storylines. Not unless Quntin Taranatino directs.
