As you mention, org-mode does not make use of the echo area to show export errors. Instead, it dumps all output that is produced during LaTeX export to a buffer called *Org PDF LaTeX Output*. If you want to get information about why the export process failed, you can switch to this buffer and search for error (or even warning).
Example
Contents of .org file:
* Heading
\begin{algorithm}
...
\end{algorithm}
Contents of *Org PDF LaTeX Output* buffer (abbreviated to show relevant parts only):
This is pdfTeX, Version 3.14159265-2.6-1.40.15 ... (preloaded format=pdflatex) ...
LaTeX2e <2014/05/01>
...
LaTeX Warning: No \author given.
(.//beamer.toc)
! LaTeX Error: Environment algorithm undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.32 \begin{algorithm}
! LaTeX Error: \begin{document} ended by \end{algorithm}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.33 \end{algorithm}
...
In this case, the output tells us that the error was caused by the \begin{algorithm} declaration in line 32. Note that specifications of line numbers (l.32, l.33, etc.) refer to the .tex file, not to the original .org file.