Nutshell: Not bad, but surprisingly pointless. This installment's theme comes about five months too late.
Cruising through the Delta Quadrant on the ongoing journey home, the crew comes across a 20th century Earth automobile floating in space—an object whose impossible location in very distant space leads to the discovery of missing 20th century humans who somehow ended up on a planet on the other side of the galaxy.
These humans were abducted by an alien race in the year 1937 and put into cryo-stasis for over 400 years. Among the displaced humans is Amelia Earhart, whose mysterious, historic 1937 disappearance is explained in science-fiction terms by scripters Taylor and Braga. This idea is a bit atypical of New Star Trek style, resembling something that would've more likely taken place on The Original Series.
Unfortunately, there's a major flaw in the use of Amelia Earhart. Her role in the episode proves to be depressingly underwhelming, partly because the opening credits saying "Sharon Lawrence as Amelia Earhart" ruins the surprise factor from square one, but mostly because the character/historical figure is put to very little productive use. What's the point of using Earhart? It has to do with Janeway's respect of a woman who pioneered air flight, but there just isn't much depth or effort put into the idea.
Fortunately, the finding of these humans leads to an understandable story that addresses the frustration in the crew's realization that they may never see Federation space again. Through a series of plot twists and phaser fights, the Voyager crew discovers an entire human civilization on this planet. As explained by John Evansville, one of the Delta Quadrant humans (played by John Rubinstein, whose overacting leaves much to be desired), this civilization began after the descendants of the abductees revolted and overthrew their captors—an alien race called the Briori.
With an entire human civilization and their beautiful new cities on this planet, it feels a lot like Earth. Knowing the possibility exists that they may never again see Earth, some of Voyager's crew members begin thinking about staying behind on this planet. Now Janeway must decide whether the Voyager should continue, or whether the crew should end their mission and rebuild their lives in the Delta Quadrant.
"The 37's" has a fairly relevant theme in the context of Voyager being far, far from home. But shouldn't this episode have come earlier in the series? Considering we are some 16 episodes into the series, it's not really timely to do an episode like this. This is a problem that undermines the show. It's hard to care about the story, because we know the outcome: The crew will press on, because they really want to see Earth again, and there's just no comparison between Earth and this new isolated civilization.
But what about those beautiful cities Evansville speaks of? We never get to see them. Instead we get a scene in the Voyager conference room, a cut, and then a Captain's Log saying "Those were beautiful cities..." A matte painting could've made all the dramatic difference here. Apparently it wasn't in the budget. Instead there's a nifty but pointless special effects sequence of the ship landing on the planet. Why? Because this week there's too much interference to use the transporters or something. Whatever. Landing the ship has zero relevance to the story, but what the hey?
"The 37's" is not a bad story, so much as an untimely one. The cast feels sincere and genuine throughout the show. Heading into the second season, however, Voyager needs to get over being homesick.