Is there any link between sea-water inflitration into groundwater and nitrate?
While the context and specifics would likely vary from site to site, the situation along the Gaza strip may be due to contamination of the Mediterranean Sea.  I am unsure of natural levels of Nitrate in ocean water, but I know that it is possible to contaminate water, independent of it's salinity.

Nitrate, like other water-soluble ions, ultimately is transported from the land to the oceans via the hydrologic cycle.  Waste from marine organisms also likely contributes nitrate.  This paper talks on the content of nitrate in ocean water. For more information on the various major constituents of sea water, check out this site.

There has been reported incidence of sewage draining into the Mediterranean, which would explain nitrate contamination in conjunction with sea-water intrusion.