The problem is simple: You’ve got overlapping vertices which may visually appear to be singular.
The easiest way to discover the issue of duplicate vertices is through the Boolean tool. That said, sometimes it can backfire and create vertices very close together or even in the same spot! This can cause a variety of issues, such as undesired deformations or unexpected difficulties with tools like the knife tool or modifiers that affect the mesh.
It may be hard to notice this issue, but it usually becomes evident when another tool doesn’t work properly. For example, trying to subdivide an edge may not work if either end has multiple vertices.
Checking for Double Vertices
One way to check is to look at the top of the window where it shows the number of vertices, edges, and faces in the scene. In this case, we’re looking at vertices (labeled as “Verts”), and in the picture above, you can see how two vertices can appear as one.
First, turn off the “Limit Selection to Visible” function, which is located on the lower bar of the viewport. You can then hold ‘B’ and right-click in order to drag and draw a selection box around the vertex you suspect is duplicated. This allows you to see through the mesh and select vertices on the back-faces.
The solution is fairly simple: Using the “Remove Doubles” tool, you can easily collapse the duplicate vertices into singles. This is done in three steps:
The doubles are now removed, and you can go about your day!
Note: This is also an important final step when creating an STL for 3D printing.
Feature image source: CGCookie
License: The text of "Blender: Remove Doubles – How to Remove Double Vertices" by All3DP is licensed under a Creative Commons Attribution 4.0 International License.