Another suggestion that others have mentioned as a way to quickly check a network dataset in problem areas where there does not seem to be a route found is to use the "Create a Service Area" function in Network Analyst. When doing so, intentionally put in a very large distance so it will try to create a Service Area for the whole dataset. Also, be sure to check "on" the option for "Generate Lines".
Then run it. After it is run, first check the overall Service Area to see if it matches the expectation. Disconnects of the data will result in a road network without a Service Area polygon. Then zoom in to these spots and use the Generated Lines to see where the "break" is. Note that the break may be due to either a disconnect and/or a Network-specific Attribute set wrong. For an example of the latter, "Oneway" set for a one-way street, but in the wrong direction, so the routing cannot happen.
Chris Donohue, GISP