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][1]; oddly in the html article the superscript numbers are there but the notes are missing.) Some highlights:

* A [2009 meta-analysis][2] 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][3].


  [1]: http://cspinet.org/new/pdf/cover_-_salt.pdf
  [2]: http://www.bmj.com/content/339/bmj.b4567.full
  [3]: https://skeptics.stackexchange.com/questions/415/is-salt-really-white-death/417#417