I don't feel much of a need to recap the story. I'm pretty sure you all know the story of Jackie Robinson. I'll bet many of you have already seen the movie.
If you haven't, you should.
The movie stayed relatively close to the truth, though this article points out several places where the truth and the movie diverged. Boston Globe writer Bob Ryan also disputes some of the scenes in the movie.
One thing the movie really seems to get right was the look. The producers seemed to have a pretty good eye for detail. Everything seem to make you feel like you were in 1946 and 1947.
The uniforms were baggy flannel.
The gloves were small.
Hitters didn't wear helmets.
And the ballparks were awesome!
For me, there's nothing worse than a baseball movie that looks fake. 42 is definitely not one of those movies.
As far as Cubs connections go, there aren't any obvious ones from the movie. The Pirates, Phillies, Reds, and Cardinals were all shown in less than a positive light for incidents (some real, some embellished by Hollywood) from 1947. The Cubs, thankfully, went unscathed.
In fact, when Robinson made his Wrigley Field debut, a crown of 46,572 jammed into the friendly confines. That is the most fans ever to watch a single game in the ballpark's 99 year history and will probably never be broken. I've got the Trib article from the game here.
The only other Cubs connection would be...
...Leo Durocher, who would have been Jackie's first big league manager if he hadn't been suspended for the season. Of course Leo would go on...
... to manage the Cubs in the late '60s and early '70s