Is there are way to annotate pdfs with LaTeX?

Here's an example using pdfpages to load the PDF as a background with TikZ to draw on top of it. The following code will complain about a missing image (tikzmark_example.pdf) but hopefully will give you the idea of what I was saying in the comments. I've left the grid in place as that's how I figure out the coordinates. This is adapted from code I use to "fill in" PDF forms by writing on top of them - in other situations I'd probably end up with a different set of helper macros to make it easier to place the annotations.

\documentclass{article}
%\url{http://tex.stackexchange.com/q/85651/86}
\usepackage[svgnames]{xcolor}
\usepackage{pdfpages}
\usepackage{tikz}

\tikzset{
  every node/.style={
    anchor=mid west,
  }
}

\makeatletter
\pgfkeys{/form field/.code 2 args={\expandafter\global\expandafter\def\csname field@#1\expandafter\endcsname\expandafter{#2}}}

\newcommand{\place}[3][]{\node[#1] at (#2) {\csname field@#3\endcsname};}
\makeatother

\newcommand{\xmark}[1]{\node at (#1) {X};}



\begin{document}

\foreach \mykey/\myvalue in {
  ctsfn/{Defined in Week 1},
  metsp/{Defined in Week 3},
} {
  \pgfkeys{/form field={\mykey}{\myvalue}}
}

\includepdf[
  pages=1,
  picturecommand={%
    \begin{tikzpicture}[remember picture,overlay]
%%% The next lines draw a useful grid - get rid of them (comment them out) on the final version
    \draw[gray] (current page.south west) grid (current page.north east);
\foreach \k in {1,...,28} {
      \path (current page.south east) ++(-2,\k) node {\k};
}
\foreach \k in {1,...,20} {
      \path (current page.south west) ++(\k,2) node {\k};
}
%%% grid code ends here
\tikzset{every node/.append style={fill=Honeydew,font=\large}}
\place[name=ctsfn]{14cm,17cm}{ctsfn}
\place[name=metsp]{11cm,9cm}{metsp}
\draw[ultra thick,blue,->] (ctsfn) to[out=135,in=90] (9cm,17.3cm);
\draw[ultra thick,blue,->] (metsp) to[out=155,in=70] (6cm,9cm);
    \end{tikzpicture}
  }
]{tikzmark_example.pdf}

\end{document}

The result of the above is:

Although there might be a way to comment third party PDFs by using LaTeX, this is not a usefull way.

There are lots of software to deal with your needs, but more on the windows side. Under Linux, I employ flpsed, http://flpsed.org/flpsed.html.