What this coin looks like (obverse, reverse, mint mark location, special features, etc.): There were multiple varieties of the 1824 Capped Bust Half Dollar. The most common variety is simply the Normal Date type with no errors and no special features.
One variety features what is likely an 1824/2/0 or 1824 struck over 1822 which was struck over 1820. This is known as the "4 Over Various Dates" variety - as the 4 is struck over a jumbled mess of multiple dates. It is very easy to spot this variety and it's possible that more dates are mixed in as well
The next major variety is the 1824/1 overdate featuring an 1824 date struck over an 1821 date (4 over 1) - which resulted in a very subtle part of the underlying "1" being seen just to the upper-right and upper-left part of the "4". Collectors often confuse this with the 1824/4 (4 over 4) varieties. The way to distinguish the difference is to view the spacing between the "2" and "4". The two numbers are nearly touching with very little space between them in the 1824/1 variety.
The 1824/4 half dollar variety actually has two sub-varieties. Both of them have an 1824/4 repunched overdate - likely an attempt by engravers at the Mint to spread the numbers out further. The Type 1 variety features a small portion of the top of the first underlying "4" just to the left of the second "4". The Type 2 variety features the same portion of the first "4" appearing to the left of the second "4" - but also has two line features at the bottom-left and bottom-right of the 4 extending towards the rim. The difference between the 1824/4 Type 1 vs Type 2 half dollar can also be distinguished more easily by viewing the spacing between the "2" and "4" in the date. The Type 1 has the numbers closer to each other while the Type 2 has the numbers further apart.
The difference between the 1824 Normal Date vs 1824/2/0 (4 over various dates) vs 1824/1 vs 1824/4 varieties is depicted below in the example comparison diagnosis chart: