Outer door handles.

Any 63-66 A-body door handle will work. Probably just a broken/rusted clip.

Or you can pick up new ones here,
http://www.ebay.com/itm/NEW-63-64-65-66-Cuda-Dart-Valiant-Barracuda-Outside-Door-Handles-MADE-IN-US-/370912257111?pt=Vintage_Car_Truck_Parts_Accessories&fits=Year%3A1966%7CMake%3ADodge%7CModel%3ADart&hash=item565c17e457&vxp=mtr#ht_337wt_679