I've gone ahead and set up a new linkspage with some more of the 16th century damask linen tablecloths I've found; you can find it at http://larsdatter.com/damask-table-linens.htm
> You know - I still like working a little embroidery on my table
> linens though. While not entirely authentic - a nice embroidered
> border makes me feel very happy and having matching table napkins
> with a little embroidery in one corner to identify each user - also
> makes me feel good. I do tend to use a pattern/design from the
> time period with correct period colours and correct fabrics too.
> I might not enter it in an A&S competition, but when setting out
> a feast table I love the look.
Embroidered table linens are certainly not non-period, but it's less common, even in wealthier households (where, if we're in the 16th century, the damask linen could be custom-woven for the household's needs, anyway). There are examples of embroidered table-carpets from the 16th and 17th centuries -- one of the most well-known of these is the Bradford carpet, which you can find at http://en.wikipedia.org/wiki/Bradford_carpet
-- though again, these are table carpets and not really table linens, so it's unlikely that food would have been served directly on top of this.
There's a rather nice little textile photographed in "Medieval Craftsmen: Embroiderers" that seems to be an embroiderer's interpretation of one of the Perugia-style brocaded linens (again, see http://larsdatter.com/perugia-tablecloths.htm
for several examples). I've done an embroidered table-covering in this sort of style as well. It's easy to re-create the Perugia brocaded ornamentation with a needle and thread in a monochromatic embroidery technique.
Speaking of monochromatic embroidery, another style that I think would be eminently suitable for a southern Italian table would be the voided-work styles; most of the extant examples that remain are just the embroidered strips, but IIRC there are sufficient examples of 16th & 17th century Italian household linens with this style of embroidery that it would not be completely out of the question. This is the form of cross stitch that modern embroiderers often call Assisi work; you can see several period examples at http://www.larsdatter.com/voided-work.htm
Also in terms of Italian textiles, there is the lovely (and potentially embroidered) table-covering in this mid-16th century portrait by Bacchiacca: http://www.getty.edu/museum/research/provenance/provResearch?handle=plid&id=777
Like the table-carpets in various portraits at http://larsdatter.com/carpets.htm
this also seems to be used as a table-covering in a non-culinary context.
It does make sense, though, if you think about it; as with undergarments, tablecloths would need to be cleaned very regularly, preferably bleached white to indicate their quality and cleanliness. (See http://www.larsdatter.com/laundry.htm
for some images of how sun-bleaching linens was done.) For a household tablecloth that would get used under food, white linen would make quite a lot of sense. :)