This probably isn't the most efficient way to do this, but using a map is simple and short:
var uniqueValues = d3.map([])
jsonStr.forEach(function(d){ uniqueValues.set(d.date, d); });
newJsonStr = []
uniqueValues.forEach(function(d){ newJsonStr.push(uniqueValues.get(d)); });
The result:
[{"date":"2011-11-14","value":0.1121},{"date":"2011-11-25","value":-0.0231}]