How far should a programming language aware diff go?

It really depends. Whitespaces are something most languages don't care. The only people who care are enforcing style guides. Level 2 is the same but there it start to get more critical, because can you be sure that it makes no difference? Level 3 is critical. While it can help to eliminate code that probably didn't caused the problem, it makes a difference. In code review this can make a difference. If a specific Hex number is well known, like of example 0x4711 and someone changes it to 18193 or even Binary, information to the programmer gets hidden. And even in style this makes a difference. When you have a flag Enum, the thing to use is binary or bit shift, because both is readable. Decimal is readable to a certain point. 4 bytes is fine but at the 5th I don't know them by heart and can't even spot them. Level 4 is irrelevant, when its on top of the file and bothering to hide it, is not necessary. Also this can be relevant. For example a while ago at our company we had code that needed to work with .NET 2 and we had parts with .NET 4 and at some point, new files had the using for LINQ, that isn't available in .NET 2. This happened a lot.

The best solution is to have options and let the person using it decide. What I'm missing is to add my own ignore list. For example with our XML files, we have a date in them. The XML Class is badly written, because instead of having one date attribute for the first node, we have them on all. This is pretty irrelevant to show in a diff, because its not even used. Rewriting the Class is a big task, because its a core feature and can break everything, when one thing is missed.