The argument of \mathcal should be an uppercase Latin-alphabet letter. With some math fonts -- though not with mathpazo -- the arguments of \mathcal can also be lowercase Latin-alphabet letters. For sure, though, I know of no math font package that enables \mathcal to operate meaningfully on greek-alphabet letters.
In short, do change \mathcal{D_\rho} to \mathcal{D}_{\rho}.
Aside: \mathcal{\rho} is a user error. Just because LaTeX doesn't crash and burn when it encounters \mathcal{\rho} is not proof that it's an instruction that has a chance of producing something meaningful. The fact that \mathcal{\rho} outputs \rho if the mathpazo package is not loaded simply means that the default math font (Computer Modern Math) has been trained to simply ignore the \mathcal wrapper if its argument is \rho, and maybe other Greek-alphabet characters too. It is not a sign that it's meaningful to run \mathcal{\rho}.

\documentclass{article} % or some other suitable document class
\usepackage[sc]{mathpazo}
% 'mathpazo' is close to being obsolete. Do consider using:
%\usepackage[osf]{newpxtext}
%\usepackage{newpxmath}
\begin{document}
$\mathcal{D_\rho}$ vs.\ $\mathcal{D}_{\rho}$
\end{document}