I'm sorry but you wrongly used the Chinese symbol.
U+25CB (○) is a 'white circle', but NOT a Chinese character. You should, instead, use U+3007 (〇) for a 'ideographic number zero'.
xeCJK does not treat U+25CB as a CJK symbol, so in your document Latin Modern Roman font is used and no glyph is output.
The two symbols look very similar. Even some Chinese misuse them. However, in some fonts, e.g. Microsoft YaHei, the two look quite different:

CJKnumb package from the CJK bundle is often used to produce CJK numbers and digits. Although it is not designed for xeCJK, xeCJK has a CJKnumber option to fix the problems and makes it available:
\documentclass{article}
\usepackage[CJKnumber]{xeCJK}
\setCJKmainfont{PMingLiU}
\begin{document}
二〇〇二年
\CJKdigits{2002}年
\end{document}
Also, you can use 李清's new zhnumber package to produce CJK numbers and digits. It works fine with xeCJK. Example:
\documentclass{article}
\usepackage{xeCJK}
\setCJKmainfont{PMingLiU}
\usepackage{zhnumber}
\begin{document}
二〇〇二年
\zhdigits{2002}年
\end{document}
zhnumber is a modern alternative of CJKnumb. We plan to use zhnumber instead of CJKnumb for future versions of ctex bundle and other Chinese tools.
For the symbol usage, you can certainly use ○ and ● as you wish. However, you should specify a NON-CJK font rather than a CJK font. Say, you can use \setmainfont to set a font with these symbols:
\documentclass{article}
\usepackage{xeCJK}
\setmainfont{Linux Libertine O} % for solution 1
\newfontfamily\simsun{SimSun} % for solution 2
\setCJKmainfont{SimSun}
\begin{document}
\section{Use a western main font with Unicode symbol support}
十六字令
天。休使圆蟾照客眠。人何在?桂影自婵娟。
○。[●]●○○●●○。○○●,[●]●●○○。(Linux Libertine)
\section{Use a Chinese font as a normal font}
{\simsun ○。[●]●○○●●○。○○●,[●]●●○○。}(SimSun)
\section{Configure xeCJK to treat the symbols as CJK symbols}
\xeCJKsetcharclass{`●}{`●}{1}% DO NOT use this
\xeCJKsetcharclass{`○}{`○}{1}% DO NOT use this
○。[●]●○○●●○。○○●,[●]●●○○。(SimSun, without affecting brackets)
\end{document}
But remember: don't use U+25CB as a CJK number, you should modify the source code.