What's With The 1982-D Quarters? Is This An Error?

Yes a weight would be useful. Also, is the reeding intact along the edge? Normally, when one side of the coin is slightly off center like this, it is due to a mis-aligned die, but I'm not convinced of that yet.

It is normal for that year. The reason why is that the master hub was swelling outwards. Thus making the design larger than the die specs. Thus when it was machined all of the dies were all created with the issue of the swell hub, on down the line. All of them looked that way that year. In 1983 they created a new master hub and fixed the issue.

This didn't happen quickly, but over time:

Note the devices were moving closer and closer each year, until 1983 when the mew master hub was created:

Note how the bust is larger on the 1982 compared with the 1983. This was progresive and then with the new master hub, the size went back to where it should be in size.
So the issue was with the master hub (top on the list I posted above) and the design was passed on down to all the quarter dies that year.