This issue is not related to tikz but is an issue with minipage.
In a minipage, the parameters \parskip and \parindent seem to be reset.
So you can adapt the solution from How to preserve the same parskip in minipage to define a minipageparskip environment which preserves the \parskip and \parindent. Here is a before (in red) and after comparison:

References:
Code:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes,backgrounds,arrows}
\usepackage{tabularx}
\tikzset{mybox/.style= {draw=black,fill=black!5,thick,rectangle,rounded corners,inner xsep=40pt, inner ysep=14pt}}
\newlength{\currentparskip}
\newlength{\currentparindent}
\newenvironment{minipageparskip}[2][]
{\setlength{\currentparskip}{\parskip}% save the value
\setlength{\currentparindent}{\parindent}%
\begin{minipage}[#1]{#2}% open the minipage
\setlength{\parskip}{\currentparskip}% restore the value
\setlength{\parindent}{\currentparindent}% restore the value
}
{\end{minipage}}
\begin{document}
\begin{tikzpicture}[transform shape]
\node [mybox,fill=red, fill opacity=0.2, text opacity=1] (box) { \begin{minipage}[t!]{0.75\textwidth}
Then we look for \textbf{clues}.
Okay, this is a good time to find any direction words. Those are words that tell you how the two blanks are related.
Here's one: while.'' The wordwhile'' sets up a contrast between the first and second blanks. We know from Step One that both are people who work with stars, and now we also know that they are different kinds of people.
\end{minipage} };
\end{tikzpicture}
\begin{tikzpicture}[transform shape]
\node [mybox] (box) { \begin{minipageparskip}[t!]{0.75\textwidth}
Then we look for \textbf{clues}.
Okay, this is a good time to find any direction words. Those are words that tell you how the two blanks are related.
Here's one: while.'' The wordwhile'' sets up a contrast between the first and second blanks. We know from Step One that both are people who work with stars, and now we also know that they are different kinds of people.
\end{minipageparskip} };
\end{tikzpicture}
\end{document}
tikzand see the same problem in aminipage. – Peter Grill Apr 25 '13 at 04:05