Consider the following code:
\documentclass[twocolumn]{article}
\usepackage[margin=1in]{geometry}
\usepackage{lipsum}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{breqn}
\usepackage{amsmath} \delimitershortfall=-1pt
\usepackage{mleftright}
\usepackage{color}
\begin{document}
\lipsum[3-4]
\textcolor{red}{{\ttfamily \textbackslash mleft} and {\ttfamily \textbackslash mright} inhibits the breaking between delimiters inside {\ttfamily dmath}:}
\begin{dmath*}
\mathcal{O}(f) = \mleft\{ t \hiderel{:} \mathbb{N} \hiderel{\rightarrow} \mathbb{R}^+_0 \hiderel{\mid} \exists c \hiderel{\in} \mathbb{R}^+ \wedge \exists n_0 \hiderel{\in} \mathbb{N} \wedge \forall n \hiderel{\geq} n_0 \wedge t(n) \hiderel{\leq} c \, f(n) \mright\}
\end{dmath*}
\textcolor{blue}{{\ttfamily \textbackslash left} and {\ttfamily \textbackslash right} produce a good results but {\bf is preferable in many equations always use} the {\ttfamily \textbackslash mleft} and {\ttfamily \textbackslash mright} commands:}
\begin{dmath*}
\mathcal{O}(f) = \left\{ t \hiderel{:} \mathbb{N} \hiderel{\rightarrow} \mathbb{R}^+_0 \hiderel{\mid} \exists c \hiderel{\in} \mathbb{R}^+ \wedge \exists n_0 \hiderel{\in} \mathbb{N} \wedge \forall n \hiderel{\geq} n_0 \wedge t(n) \hiderel{\leq} c \, f(n) \right\}
\end{dmath*}
\lipsum[1-5]
\end{document}
Output:
Are there any solution or modification that allowed to use \mleft and \mright correctly inside \dmath?
breqn
redefines more or less everything related to math typesetting in TeX. Then you load Heiko's package and he redefines stuff again, but aimed at a normal tex setup. It's no doubt possible to rewrite mleftright in breqn style, but not working together should be the expected behaviour.