I work with the combination of Blender and Pepakura for creating paper models. Sometimes it so happens that a seemingly perfect model in Blender has unconnected edges in Pepakura. These show up as red lines and result in a model where two faces are not connected although they should be.
There are several causes. One is that one or more vertices are duplicated, i.e. that two vertices are positioned at the same location. To fix this, go into Edit Mode, then press A to select all vertices, then press W and “Remove doubles”.
If that doesn’t help, in Edit Mode press ctrl+alt+shift+M. This selects non-manifold edges, i.e. edges where the model is open. Then press alt+M in order to merge the affected vertices.
If the problem still persists, you can recalculate the normals. Go into Edit Mode, select everything (press A), then press ctrl+N. The problem in this case is that each face of your model has an orientation. You can think of it as the “front” and “back” of the face. The so-called normal is a vector perpendicular to the plane of the face. Since the face has two sides, the normal can point in either of two directions. If a model consists of a contiguous surface where the normals of some faces are oriented differently than those of the other faces, Pepakura assumes that the surface isn’t actually contiguous (and rightly so).
In most cases, ctrl+N solves this problem automatically. However, there are some models which do not enclose a space completely, but which contain openings. In such a case, Blender may fail to orient all faces properly. You will see the problem in Pepakura by two sets of faces, one showing the texture (or face color) on the “outside”, and one showing it on the “inside” (double quotes, as technically there is no such thing as in and out for a model with openings). You can switch the orientation of the normals manually in Blender – here is a tutorial.