I've read where people commented on how a photo was edited to block out someones face or a part of a picture that it was done incorrectly and that the original data could be restored.

What is the method for doing this?  I am somewhat versed in Photoshop, but this is not something that I've had to deal with. I've got a picture someone sent to me, because they know I do a lot with PS, that has part of the item blacked/blocked out in a sales add.  Not by them, but by the seller. We're thinking it might cover part of the item that would make him not want to buy it.

How can I inspect this photo and check to see if there is a possiblity to restore that portion of the photo?

if what you've got is a .jpeg from the seller, I don't think its possible.  If you had the orginal file with layers intact i think it'd be possible.  but once the layers are flattened and the pic is exported I think all that data below it is lost.  

just some random advice from a guy on the interenet.  I will admit i'm not an expert.  maybe i'm wrong.

What's the file type?

I can't think of any thing that would do that unless you have the original PSD/cr2 file or recover the deleted photo from a hard drive.

My solution would be the same as I apply to everything else:  If they are keeping something secret, ask them what it is, and if they won't tell you, go elsewhere.

This is pretty much the plan.  It's a .jpeg I have.  I didn't think it was possible, but I thought I had read something about it in a thread where someone had posted a picture with a gun s/n blurred out or a license plate blurred out but the photo data was still there somehow.

This

 

In Photoshop, make a round marquee centered on the centerpoint of the twirled image, then full negative setting on the twirl filter.
If it's been painted over, like others have said, you can play with it but there is probably nothing there to undo.

Many box/radial blurs (changing info) can be undone. Solid colors (destroyed info) can not since the original pixels are gone.