What this coin looks like (obverse, reverse, mint mark location, special features, etc.): There are numerous varieties and sub-varieties of the 1834 Capped Bust Half Dollar. The major varieties can be distinguished first by the size of the numbers in the 1834 date. One has a smaller date and the other has a larger date - and there is a easily recognizable difference as depicted above in the example comparison image.
The small date variety can be divided into sub-varieties based on the size of the stars on the obverse of the coin. One variety has small stars which are noticeably smaller with much more spacing between the rim of the coin and the liberty bust portrait (especially the spacing between the bottom-left star and the liberty bust). The large star variety has larger stars and there is narrower spacing between the stars and the rim of the coin. The difference between the small stars vs large stars is depicted below in the example comparison image of the coins:
Next we look at the reverse of the coin - particularly the sizing and spacing of the letters in the words "UNITED STATES OF AMERICA" and the "50 C." denomination. The "small date" variety will always have smaller letters. Although the "large date" variety can be classified into the "small letters" and "large letters" sub-varieties. The small letters are easily seen to be smaller and have far greater spacing between them and the rim of the coin - and they are even smaller than "small letters" varieties of previous years. The "large letters" variety has letters that are of similar size to those in previous years with less spacing between the letters and rim. The difference between the 1834 small letters vs large letters half dollar varieties is depicted below in the example comparison image: