Is there a way to check a mesh for problems? Is there a way in Blender to check a mesh for missing or duplicate faces, mesh abnormalities, or other issues that might cause problems when it is exported and used as data for a real-time application such as a game?
There's an old way. In edit mode, select nothing with A and then hit ctrl alt shift M to select non manifold verts or edges. These are edges that do not have exactly two faces connected to them. If nothing gets selected, your mesh is pretty solid.

Try it with vertex select or edge select. Both modes provide insight.