1. Methods getRunStart, getRunLimit works wrong (or spec is incorrect).
See example in attach (it big to show it there)
Try to uncomment string in example:
a) replace attrString.addAttribute(attrs[0], obj, 11, 20);
to it's analog (from spec, because value doesn't change)
        attrString.addAttribute(attrs[0], obj, 11, 15);
        attrString.addAttribute(attrs[0], obj, 15, 20);
note, that result will differ from real changing values as next
        attrString.addAttribute(attrs[0], obj, 11, 15);
        attrString.addAttribute(attrs[0], new String("$"), 15, 20);
b) add (from spec nothing changes)
        attrString.addAttribute(attrs[2], null, 40, 45);

2.
Difference between situation when Attribute is not defined (no such key), and
is defined with value == null is unclear and is not same to all methods.
The result of all method excluding
public Object getAttribute(AttributedCharacterIterator.Attribute attribute)
will differ for null values and no values.
But this differnce can't be checked with getAttribute.
I've added shorter version of example.

The problem is that implementation could consider equal attributes as different
and report incorrect boundaries. According to spec it does not matter how you add attributes
for method getRunLimit and getRunStart.

These two string accorsing to spec should be
attrString.addAttribute(attrs[0], obj, 11, 15);
attrString.addAttribute(attrs[0], obj, 15, 20);
equal ot this
attrString.addAttribute(attrs[0], obj, 11, 20);
however it does not. (The 15 should not be any boundary)
You could change variants in tests and check results.