The three sentences
1) Das hätte anders gemacht werden können.
2) Das konnte anders gemacht werden.
3) Das hat anders gemacht werden können.
are all proper German sentences, while I consider 1) to be the most idiomatic one in terms of style. They differ only very slightly in meaning. The nuances are so small that I think it is fair to say that pragmatically there is no semantical difference. Let's have a closer look at the underlying grammatical constructions to catch these differences:
1) is the only form to use the subjunctive form (Konjunktiv). This use of Konjunktiv is putting a slightly stronger emphasis on the fact that it is an irrealis that is been talked about. However, the other forms do not really miss this information, because changing a situation from the past is widely considered an impossible thing anyway. So, using the Konjunktiv to express this is more a matter of emphasis here. But as I mentioned already, pragmatically this is irrelevant.
2) is the only form in Präteritum tense (konnte) while the other forms are in Perfekt tense. The difference between Präteritum and Perfekt are subtle in German. In most cases, Pärteritum and Perfekt are semantically interchangeable and the difference between them is rather a matter of style than one of semantics. This is the case here as well.