The first problem is that the index rolls up objective and subjective measures into the same number:
For a number of indicators, the sustainability value can be determined objectively. For instance, the number of undernourished people has to be 0 (indicator 2), or the percentage of people with access to safe drinking water has to be 100 (indicator 3). This reasoning applies for indicators 2, 3, 4, 5, 6, 15, 17 and 22. However, some might question why the gender equality has to be 1. So even in this rather obvious case, some subjectivity is included.
For the remaining indicators the sustainability value is less obvious and probably cannot be determined in an objective manner. When is population growth sustainable? If the number of inhabitants stays constant? Or only when it declines? And at which percentage does it have to decline to be sustainable? Or when is income inequality sustainable? Moreover, the sustainability value of an indicator may vary over time. For instance population growth: currently our planet seems to be rather overpopulated. However, it can very well be that our view on this issue will change in the future.
For indicators 18, 20 and 21 an educated guess of the sustainability value could be made, as explained in the next paragraph. If even an educated guess is not reasonably possible, the highest value (best case) of the 151 assessed countries for that indicator is considered the sustainability value, while the lowest value (worst case) is assumed to represent no sustainability at all.
The second problem follows from the first: this single number is then presented as authoritative. Those who disagree with the structure or objective of the index will point to this conflation to discredit the entire index, including those parts that are objectively incontrovertible.
I much prefer the idea of a multi-element report card, with the objective and subjective components clearly broken out.
On edit: I don't disagree with the overall effort -- having a measure of sustainability is always a good thing for public awareness. This is similar to the "ecological footprint" concept. It's useful in much the same way, but suffers from many of the same shortcomings.