I'm close to give up my fight for MnSymbol in unicode-math. I realized I already replaced so many missing and faulty characters, that there is barely something left of MnSymol. So probably I will just go the other way around in the future, use a different math font and replace the symbols I don't like with MnSymbol.
However, please allow one last question before I carry MnSymbol to his grave:
Obviously the full stop is missing in MnSymbol:
$\Bigg[\bigg(\big[ 42 \big]\bigg)\Bigg].$

When I replace the full stop with a different font, all brackets get followed by a \cdot:
\setmathfont[range={"002E} ]{XITS Math}

which won't happen if I replace the whole math font:
\setmathfont{XITS Math}

Besides looking for a solution, I actually would like to know
Why?
I'm replacing a certain unicode character and others are affected as well, that does not make any sense?
Full MWE:
\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmathfont{MnSymbol}
\setmathfont[range=\mathup/{num,latin,Latin,greek,Greek}]{Minion Pro}
\setmathfont[range={"005B,"005D,"0028,"0029,"007B,"007D} ]{XITS Math} % brackets
\begin{document}
$\Bigg[\bigg(\big[ 42 \big]\bigg)\Bigg].$
\setmathfont[range={"002E} ]{XITS Math}
$\Bigg[\bigg(\big[ 42 \big]\bigg)\Bigg].$
\setmathfont{XITS Math}
$\Bigg[\bigg(\big[ 42 \big]\bigg)\Bigg].$
\end{document}
For future reference:
A full solution can be found here, but
\Udelcodenum`.=1073741824
needs to be changed to
\Udelcodenum`.=0
Underfull \hbox (badness 10000) in paragraph at lines 16--17:( – David Carlisle Apr 22 '15 at 11:00\setmathfont[range={"002E} ]{XITS Math}instruction. – egreg Apr 22 '15 at 11:30\Udelcodenum.=0` works for me too! Thanks for the link! – Robert Seifert Apr 22 '15 at 11:40