Only two die varieties are known for the 1812 Half Eagle. Both varieties share the same obverse, but differ on the reverses. One variety has a widely spaced 5D in the denomination (BD-1); the other has a closely spaced 5D (BD-2). Though the spacing on the Wide 5D is dramatic, the two reverses can also be told apart by the position of the I of PLURIBUS. On the Close 5D, the I is under the right side of the T; on the Wide 5D, the I is under the left side of the E.
Both varieties are scarce, but the Wide 5D is definitely the more common of the two.
Numerous MInt State examples exist of the 1812 Wide D Half Eagle, including several Gems. The best example is the PCGS MS66+ -- formerly of the Pogue Collection.