What I find this boils down to is a matter of definitions. Not so much the definition of "adjacent", but of "object", "square", and "unoccupied square" as they pertain to targeting.
Much of this discussion revolves around using a target definition of "object" (as nobody has yet tried to use "creature") to, in some way, target a occupied or unoccupied square. This, at least to my mind (ymmv), meets with varying levels of success:
"I target the chair/barrel/[tiny or larger object in the square]."
This fits perfectly into the definition of "Object" in regards to targeting. What is more, there are relatively specific rules in the DMG for targeting objects from size "tiny" to "huge".
"I target the pebble/bit of lint/leaf/[smaller than tiny object in the square]."
Should be perfectly do-able, but runs into two issues. As there is no set AC for smaller than "tiny" (nor larger than "huge"), the solution can vary from DM to DM. Also, this can start a bizarre escalation if overused: After too many uses, angry DM starts declaring that the rooms are perfectly spotless, with nary a mote of dust or loose pebble to be found. Player responds by bringing bags of pebbles/dirt/etc to spread through an adventure. The whole thing becomes relatively ridiculous.
"I target the square (he's standing in)."
I seem to find this one a bit more cut and dried than others. We are now using "object" to refer to an occupied or unoccupied square.
As far as I can tell by the books, the only thing that can target an occupied square (not an object in the square, but the square itself) is an Area attack. Even then, the target list deals with creatures/objects/enemies/allies.
My issue with using "object" to mean "unoccupied square" is one of definition and logic. "Unoccupied square" is already used in a handful of powers as a target. This, in itself might not be damning, as "creature" can encompass "enemy" quite handily. What causes my issue is that there are two powers that list both "object" and "unoccupied square" as targets. Regardless of the powers in question (Light and Ghost Sound), the fact remains that they used "object or unoccupied square" for the target of these powers.
If "object" could refer to an unoccupied square, why would Light and Ghost Sound not simply list "object" as the sole target?