Cannot join vertices

Hi, I am an absolute beginner to Blender and 3D so I have a little mess in my meshes and objects etc. And I have this weird problem that I just cannot join specific vertices. In Object mode they appear to be joined and faces are visible. In Edit mode, there are just holes. What am I doing wrong? Thanks for any help. I am gonna remodel it from scratch but I am curious what’s wrong anyway.

Please post the file so we can see what the problem is. The 'shots don’t give a clear idea.

Unhide any hidden mesh in edit mode with Alt+H
Remove any faces inside the mesh
Remove double vertices (select all vertices and W / remove doubles)
Recalculate face normals (select all vertices and Ctrl+N)
Flip selected faces with W / Flip Normals