DiggThis widget shown in Print module's Printer-Friendly Version

I haven't checked this module's code, but if you have access to the node variable during the placement of the digg this link, just check $node->printing and if it is TRUE don't show the link.

João Ventura

This button certainly does not make sense in a printer friendly version. The same applies for comment links and forms and other stuff that requires user interaction. A printer friendly version should only contain readable information and images. A call to strip_tags('script') in the print module before the output is rendered could be an option to remove unnecessary content added via JS.
I do not consider this a bug of the diggthis module. You cannot expect every module that adds content to nodes to make sure this content is not added by the print module to the printer friendly page.

Another solution would be to add a print.css file for printed versions of your pages and set the digg this button to hidden in this CSS file.
In print.css add:

.diggthis_button {
display:none;
}