So I am beginning to wonder if these "Unique" and "Set" item problems
are present at every patch level. Or maybe just certain items are bugged
from the getgo and no patch currently fixes it.

Thinking back, in Act I (patch 1.1, I think), I got these uniques which are good:
1. Lucky Cap
2. DeathKnight's Claw

In both cases, they both had extra abilities applied and did not have a vanilla "white" descriptive text.

Now that you mention it, I've never gotten a "set" item that was special either. But I never said anything because I figured you had to get the whole set before
you saw any abilities come out.