I found a straight forward way of solving this, with the use of JSON.parse.
Let's assume the json below is inside the variable jsontext.
[
["Blankaholm", "Gamleby"],
["2012-10-23", "2012-10-22"],
["Blankaholm. Under natten har det varit inbrott", "E22 i med Gamleby. Singelolycka. En bilist har.],
["57.586174","16.521841"], ["57.893162","16.406090"]
]
The solution is this:
var parsedData = JSON.parse(jsontext);
Now I can access the elements the following way:
var cities = parsedData[0];