I wanted to migrate from JabRef to Zotero but I first encountered the following issues:
1) All my Pdf links were lost in the process.
2) The Bibtex field "review" was not transfered. Unfortunately, this field is where I stored all my reading notes for my bibliographic entry.
3) The French diacritical marks were not imported.

Since I am probably not the only one to have these kinds of problems, I describe the fix that I used.
Note that anyone using some customized Bibtex field can modify my JabRef filter (see below) to import the field info as notes in Zotero (or any field you'd like).

The steps:
1- make sure you are using JabRef 2.4 (or later versions: http://jabref.sourceforge.net/index.php )
2- Install the Jabref plugin called "RIS export format" (this step seems odd since I'm not using this filter, but the command FormatChars of my export filter was not recognized without it). Installation info here: http://jabref.sourceforge.net/resources.php
3- Make a file called Zotero.layout in a text editor including the content at the end of this post.
4- Add your custom-export filter in Jabref: Options --> Manage Custom export
Export name= zotero ; Main layout file= path/to/your/Zotero.layout ; file extension= .txt
5- restart JabRef
6- Use file --> export in JabRef and select "zotero" as the export format
7- Make sure that the export file is in UTF-8 if you care about diacritical marks (open it with a text editor and save it in UTF-8...)
8- Import the file in Zotero. Be patient if the database was large (break it up in smaller part if you feel the need)...

You get the paths to the Pdfs and notes nicely formatted.

I'll now see if the extra functions in Zotero were worth the trouble!


=========Filter Content============
@\bibtextype{\bibtexkey,
\begin{author} author = {\author},
\end{author}\begin{editor} editor = {\editor},
\end{editor}\begin{title} title = {\format[RemoveBrackets]{\title}},
\end{title}\begin{booktitle} booktitle = {\format[RemoveBrackets]{\booktitle}},
\end{booktitle}\begin{journal} journal = {\journal},
\end{journal} year = {\year},
\begin{volume} volume = {\volume},
\end{volume}\begin{pages} pages = {\pages},
\end{pages}\begin{number} number = {\number},
\end{number}\begin{chapter} chapter = {\chapter},
\end{chapter} \begin{url} url = {\url},
\end{url}\begin{doi} doi = {\doi},
\end{doi}\begin{file} \format[FormatChars,WrapFileLinks(\x = ]{\file} {\format[FormatChars,WrapFileLinks( \p ]{\file}},
\end{file}\begin{address} address = {\address},
\end{address}\begin{publisher} publisher = {\publisher},
\end{publisher}\begin{institution} institution = {\institution},
\end{institution}\begin{howpublished} howpublished = {\howpublished},
\end{howpublished}\begin{issn} issn = {\issn},
\end{issn}\begin{organization} organization = {\organization},
\end{organization}\begin{keywords} keywords = {\keywords},
\end{keywords}\begin{note} note = {\note},
\end{note}\begin{owner} owner = {\owner},
\end{owner}\begin{abstract} abstract = {\format[FormatChars]{\abstract}},
\end{abstract}\begin{comment} comment = {\format[FormatChars]{\comment}},
\end{comment}\begin{review} comment = {\format[FormatChars]{\review}},\end{review}
}