From a controllers point of view, the part about "you're X miles from X"
is just checking a box that needs to be checked. It's probably the one
messed up the most as either 1) you clear aircraft on multiple approaches
to multiple runways (not at the same time usually) and occasionally say
the wrong fix, or 2) you don't vector much for approaches and just
screw it up once in a while. I'm willing to bet all those other items,
(heading, altitude, approach clearance) are fairly accurate most of
the time. If I'm vectoring someone on a 100nm range (200nm from one
side of the scope to the other) and I say 3 miles instead of 3.5 or 4,
I suspect I wont get too much grief over it. If so, well, there's always
arcs and PT's.

For this reason, I tell students to never rely on ATC's
distance statements to make a descent.

Unless the mileage is off by some really high amount, I'd agree with
that approach, no pun intended. I assume most of you ignore the first
part of that clearance, as that is the only part of that transmission that
really is NOT a clearance anyway. Now if they give you the wrong
airport, runway, or approach, major warning flag.
But at a big airport with 12 ILS's and even more VOR, NDB, and GPS
approaches, and all the IAF's and FAF's to go along with all of those,
which are often not the same for a given runway - I'd be willing to cut
them some slack every now and then.

Chris