Plot hole: It's stated that only objects or people infused with the chronoton serum can pass through the time barriers, which is why the equipment belts and hyposprays had to be specially modified (these wouldn't be needed if the chronotons were producing a protective field wider than the infused object). But some un-infused artificial objects, such as clothing and com-badges, can pass through them without vanishing. This is most obviously seen in the scene when Chakotay pulls the captain through the barrier, since he doesn't even wait long enough for the serum to spread throughout her entire body, yet alone to perspire into her uniform.
Plot hole: Tuvok says that he was born on Stardate 38774. But he was born in 2264, when Stardates were only counted in the thousands, not the tens of thousands. If he were really born on SD 38774, that would mean he was born only a few years before the Enterprise-D was launched.