A proviso first: I have only experienced this museum for free, because the University of Chicago for some odd reason really likes to rent the entire place for events. That being said, I've visited nearly every exhibit in the place.
The MSI is somewhat of a museum by accident. It was built for the 1893 World's Fair in Chicago and I think nobody really expected it to remain intact afterwards. (all the structures built for the world's fair were quite shoddy)
However, the museum is still standing today, so I suppose someone at least did a proper job with it. What's inside? A reasonably eclectic collection of science-museum exhibits. As with any science museum, the emphasis is pretty much on a middle to high school level of education / understanding, so real scientists will no doubt be apalled. However, it is fun - everyone should check out the coal mine exhibit, which involves a 'descent' into a coal mine and a 'mine car ride', as well as the famous U-Boat which is actually a World War II relic!
more