Section numbering in article vs. report class

Let me guess: After the switch from article to report, your \subsection is still unnumbered, but your \section suddenly shows up as "0.x A section" (which resembles the look of \subsection in article)? That is because the report class (and the book class) feature the additional sectioning level \chapter, which becomes the new top level.

\documentclass{report}

\begin{document}

\tableofcontents

% Uncomment the following line to get rid of "zero-sections"
% \chapter{Chapter title here}

\section{Section title here}

\subsection*{An unnumbered subsection appearing in the ToC}
\addcontentsline{toc}{subsection}{An unnumbered subsection appearing in the ToC}

\end{document}

EDIT: If I understand correctly, you want the effect of the following (to be added to the preamble):

\renewcommand{\thesection}{\arabic{section}}

Chapters are still numbered, but sections don't feature the chapter number. (This may confuse readers, and it may screw up the cross-reference mechanism.)

\setcounter{secnumdepth}{1} will show only Chapter (if applicable) and Section numbers. The subsections will still appear, unnumbered, in the table of contents.

To get the change to appear, you will need to run LaTeX twice