tikz-cd Extra arrow tip with start anchor on edge v0.9b

edge is a bit of a strange beast, and you need to use to here instead:

\documentclass[11pt]{article}

\usepackage{amsmath} 
\usepackage{tikz-cd}
\usetikzlibrary{arrows}

\title{}
\date{}                                          
\tikzset{
   commutative diagrams/.cd,
   arrow style = tikz,
   diagrams={>=latex}}

\begin{document}
\begin{tikzpicture}[commutative diagrams/every diagram,column sep = 3em]
       \matrix (m) [matrix of math nodes, nodes in empty cells]{
       |(A)|A\\
       |(B)|B\\
       };
       \draw[commutative diagrams/.cd, every arrow, every label,dashed] 
          (B.north east) to [bend right, dashed] (A.east);
       \draw[commutative diagrams/.cd, every arrow, every label] 
          (B) edge [bend left] (A.west);
    \end{tikzpicture}
\end{document}

I think what is happending with the edge is that there are two paths, the first a very short one from (B) to (B.north east). But I haven't yet be able to verify this.

Update: thanks to the pointer to https://tex.stackexchange.com/a/82495/15925 from Torbjørn T. this is indeed the case. In your code the main path, i.e. with the edge parts removed, is

   \draw[commutative diagrams/.cd, every arrow, every label,dashed] 
      (B.north east)
      (B);

which in the above code produces

with the strangely placed arrowhead you experienced.

The full code for this last diagram is:

\documentclass[11pt]{article}

\usepackage{amsmath} 
\usepackage{tikz-cd}
\usetikzlibrary{arrows}

\title{}
\date{}                                          
\tikzset{
   commutative diagrams/.cd,
   arrow style = tikz,
   diagrams={>=latex}}

\begin{document}
\begin{tikzpicture}[commutative diagrams/every diagram,column sep = 3em]
       \matrix (m) [matrix of math nodes, nodes in empty cells]{
       |(A)|A\\
       |(B)|B\\
       };
       \draw[commutative diagrams/.cd, every arrow, every label,dashed] 
          (B.north east)
          (B);
    \end{tikzpicture}
\end{document}