The cowl is the same from '65-'68, so the dash will bolt in.
As mentioned, you would need the 1966 column along with the dash support/brake pedal mounting bracket. Of course the '66 dash will need to be complete with the wiring harness too. You'd need to double check that they didn't move any wires around in the bulkhead connector from '66 to '68. If your HVAC system functions at all, it's going to matter that the dash matches what's in your car: A/C vs. just heat.
The other hurdle would be that it can be quite difficult to remove and install a c body dash with the windshield in place. On most of the dash styles you can just barely get an offset wrench on the heads of the bolts to get them out. I think there are one or two styles that you either can't or you have to remove the pad in order to access the bolts.
And yes, the '68 Dodge dash wasn't all that great. It's much worse after all the plastic chrome wears off and turns yellow. It costs a fortune to make those look nice again.
Jeff