You report finding the needle when there is no needle...

IllegalArgumentException would be more appropos.
Either that or "not found"

Nice math. Why not just make n a long instead of an int?

Where you say "if ( kk == 1+8n ) return true; else return false;" you could simplify to "return kk == 1+8n"

Your main loop is nice. The isOpposite( ) method could use some clean up.

dist.toArray(new String[dist.size()]) would save you an allocation.

path.toArray(new String[path.size()]) would save you an allocation.

You aren't guaranteed there is only one instance of NORTH for the == test.

It looks like most of the solutions were satisfied with O(n) performance for count( ) and depth( ). It's worth the effort (not much) to improve that to O(1).

You need to test for .. instead of . to handle decimals.

Relying on the internal structure of the scales object is pure evil. Congratulations on the purity of this answer ;-)

This kata needs a better test suite. Most of the posted solutions would fail on ftp://sports.yahoo.com/somthing?unexpected=true

Not a fan of any solution that mutates input.

Your last 0* is redundant to the first one

If you use push instead of unshift and reduceRight instead of join, this will run much faster without damaging the nice code structure.