If I am following you correctly, you would access it like this:
0 accessing the first cuePoint, 1 the second, etc. Loop through with an integer variable to collect, or you *might* be able to set your DataGrid's dataProvider to infoObject.cuePoints (haven't tried that, not sure if it would work) and set the grid's column sources to match the names in the ArrayCollection.
the data structure of you infoObject is not ideal! cuePoints is an array containing arrays. It should be an Array (or even better, an ArrayCollection) of Objects or Class instances. That way, you can easily create your dataGrid:
My suggestion is to create a class CuePoint and to add instances of this class to your cuePoints Array.
This works very well - I was making it much harder than what it it needed to be. I just created an array list and did the data grid like above.
myCuePointData = neew ArrayList(infoObject.cuePoints);