Hi Axel,
For error function there is a parameter oError can you check in debugging what information does it return. Use below code:
var oEntry = {};
oEntry.Price = "599$";
oModel.update('/Products(1)', oEntry, null, function(){
alert("Update successful");
},function(oError){
console.log(oError);
});
Look at the update method here - SAPUI5 SDK - Demo Kit