If you are looking for physical connectivity issues (not the ones caused by attributes like oneway's), you can use the Utility Network tools to find disconnected parts from some known location. Take a look at:
Find Disconnected Features in Geometric Network—Help | ArcGIS Desktop
Note that this will require you to create/build a geometric network. Once you correct your issues, you can delete that and create a network dataset for use with Network Analyst. Alternatively you can use the Service Area solver (with the lines option) to find things that are "connected". Once you have this as a selection, invert the selection to find features that are not connected.
Jay Sandhu