Is there any danger of running solid rotors in a vented rotor car? What are the differences between the two? (other than the vents)

Well they are a completely different size (thickness) so it is not simply a matter of changing the rotors. You would also have to change the calipers and the caliper brackets.It would be far easier to get the correct rotors.

Edited September 4, 201312 yr by Leeroy

I ordered them from rockauto, as an 85 brat. They came in as solid rotors. They appear to be the same size to me, and bolted up as such.

Solid rotors are thinner than vented ones.

 

Once the pads wear enough, you will most likely have one of the pads remove itself from the caliper during braking.

 

Had that happen to me. I was fortunate to be very near my driveway.

 

It is not advisable to put a solid rotor on in place of a vented one, unless you change the caliper and bracket.

I ordered them from rockauto, as an 85 brat. They came in as solid rotors. They appear to be the same size to me, and bolted up as such.

 

RA has decent custom service.  The solid rotors were discontinued in '81 or '82, so there is no reason why you should have received them for an order for an '85 Brat.  The vented are superior to the solid rotors, so you don't want to downgrade.  I doubt the caliper piston for the vented rotors can compensate for the thinner solid rotor very well, so, as others have mentioned, you would really need to swap out calipers and brackets.