There are a number of things that can go wrong when creating or importing a mesh that can be difficult to troubleshoot simply by looking at the mesh.
You can check for some common problems by using CellBlender's Mesh Analysis tool, which is found under the Tool Shelf (hit t in the 3D View Window). Hit the Analyze Mesh button.
This will tell you if the mesh is triangulated, watertight (i.e. There are no "holes" in it), manifold, and that it has outward facing normals. All of these features are essential if you want to release volume molecules inside the mesh in question. If your mesh does not meet these criteria, here are a few techniques for resolving these problems.
You can force your normals to be consistent by selecting Mesh>Normals>Recalculate Outside (or hit Ctrl-n) in Edit Mode. This will make all the normals on a closed mesh point outward.
While in Edit Mode, select Mesh>Clean up>Degenerate Dissolve. This will remove edges with no length and faces with no area. Be aware that this can introduce quads in your mesh, which you will need to convert to triangles (Ctrl-t).
Lastly, we need to clean up any non-manifold meshes. Of all the operations listed here, this is the hardest to perform since it will likely require you to actually edit the mesh by hand. In Vertex Select Mode, you can select all non-manifold faces by using Select>Non Manifold (or hit Ctrl-Shift-Alt-m).
If anything is selected after performing this operation, then you have to remove the non-manifold portions. Don't simply delete everything it selects, since you might introduce holes into your mesh. Normally an edge is only shared with two faces. If your face shares an edge with more faces, then you will have to delete one of the faces.
If none of the above issues help, you can consider using the Remesh Modifier. To preserve the shape of the mesh, you may need to increase the Octree Depth. Be careful about increasing it too much though as it can increase the number of triangles considerably.
Be sure to Apply the modifer. After the modifier is applied, triangulate your mesh (Ctrl-t).