At least in the case of mammal groups above the species level, the relationships are faily well understood by this point, thanks to the advance in molecular and genetic studies over the last couple of decades. Disputes are more likely to arise when we question how broadly we should define a particular group, and what taxonomic level it might have. (The latter, of course, are entirely artificial; the cat family is provably a 'real' thing, but the fact that we call it a 'family' rather than giving it some other rank is essentially arbitrary).
This becomes a much bigger issue when we look at animals we know only from fossils. For one thing, we will have fewer, and generally less complete, specimens to examine. Furthermore, unless they are really recent, genetic analysis is out of the question. But, on top of all of that, when we travel back in time, lines become inherently blurred. There's always going to be the question of where exactly the 'not yet X' becomes 'X', even if we had perfect information about them. Which we don't.
