What this coin looks like (obverse, reverse, mint mark location, special features, etc.): There are a few major varieties of the 1830 Capped Bust Half Dollar. The two major varieties deal with the size of the "0" in the 1830 date. One variety has a smaller and shorter "0" with more spacing between the number and the liberty bust portrait. The other variety has a noticeably larger and taller "0" with much less spacing between the number and the liberty bust portrait. The difference between the large 0 vs small 0 is depicted above in the example comparison image.
Another very rare and valuable variety is the 1830 "Large Letters" half dollar variety. This variety has larger letters in the words "UNITED STATES OF AMERICA" on the reverse of the coin. Sometimes it is difficult to distinguish the size of the small letters vs large letters - so it is often easier to look at the spacing between the words to find the difference. In the large letters variety: The spacing between the words "UNITED" and "STATES" is much narrower than the small letters variety (which has much wider spacing). In addition the spacing is also narrower between the words "OF" and "AMERICA" in the large letters variety. The "C" in "50 C." is much larger in the large letters variety. These features are depicted by the arrows in the visual example of the 1830 small letters vs large letters half dollar comparison image (Source of large letters example image is courtesy of Heritage Auction Galleries):