This may be well-known, but I cannot remember having encountered this before. Here's a minimal example:
\documentclass[12pt,a4paper]{amsart}
\usepackage{tikz}
\begin{document}
\tikzset{vert/.style={circle,inner sep=1mm,draw}}
\tikzset{edge/.style={draw=#1,very thick}}
\begin{center}
\begin{tikzpicture}[scale=2.5]
\node[vert] (a) at (1.,1.3){};
\node[vert] (b) at (1.7,1.3){};
\draw[edge=blue,out=0,in=225] (a) to (b);
\end{tikzpicture}
\begin{tikzpicture}[scale=2.5,rotate=225]
\node[vert] (a) at (1.,1.3){};
\node[vert] (b) at (1.7,1.3){};
\draw[edge=blue,out=0,in=225] (a) to (b);
\end{tikzpicture}
\end{center}
\end{document}
In the rotated picture, the line is not attached correctly to the nodes:
Is that really a bug, or am I missing something? any known fix?
transform shape
to the picture you get the correct curve but of course also a scaling of the nodes.