Signs don't look so good. See this article http://www.cspinet.org/nah/articles/salt.html, which refers to a number of recent (and not so recent) studies. (There are references to the actual studies in the PDF version; oddly in the html article the superscript numbers are there but the notes are missing.) Some highlights:
- A 2009 meta-analysis of 13 studies found that cutting salt reduces blood pressure and also lowers risk of heart attacks and strokes
- long-term exposure to excess sodium means eventual high blood pressure for 90% of Americans
- even moderate blood pressure is associated with increased risk
- there's some suggestion that elevated blood pressure may be associated with dementia
- there's suggestion that salt is harmful to the cardiovascular system directly, regardless of pressure
Note that many of the studies are newer than the 2003 paper referenced in Sklivvz's answer.