Include section number in list number

You could redefine \theenumi using \thesection:

\renewcommand*{\theenumi}{\thesection.\arabic{enumi}}
\renewcommand*{\theenumii}{\theenumi.\arabic{enumii}}

In that case omit \pointedenum, it would destroy that redefinition.

That may also be done using \thesubsection.

Alternatively, here's code using the enumitem package:

\usepackage{enumitem}
\setenumerate[1]{label=\thesection.\arabic*.}
\setenumerate[2]{label*=\arabic*.}

Using enumitem you're able to continue numbering by \begin{enumerate}[resume] if you like.

The variables governing the labels for the items in an enumerated list are \labelenumi (for the top level), \labelenumii (next-to-top level),... You can use \renewcommand to redefine them to anything you want.

I would expect this to work, but I have not tried it:

\renewcommand{\labelenumi}{\thesection.\arabic{enumi}}
\renewcommand{\labelenumii}{\thesection.\arabic{enumi}.\arabic{enumii}}

I usually resolve this with the enumerate package. I always use this package anyway to control how items are enumerated by allowing you to specify e.g. \begin{enumerate}[(1)] to have parentheses the numbers etc.. In preamble use

\usepackage{enumerate}

Then:

\section{This is section 1}
\begin{enumerate}[\thesection .1]
\item This is item 1.1
\item This is item 1.2
\end{enumerate}

\subsection{This is section 1.1}
\begin{enumerate}[\thesubsection .1]
\item This is item 1.1.1
\item This is item 1.1.2
\end{enumerate}

This solution allows you to use section numbering in enumerate only where you specify it. However if you want to do this globally I would use Stefan Kottwitz' solution above.