The 1851-O Half Dime has a relatively hefty mintage but because the majority of the coins went into circulation, few were saved by collectors. Thus, a P-Mint date with a similar mintage will be much more common and less valuable than the 1851-O. In Mint State, the 1851-O Half Dime is semi-scarce, which means it may be tough to find, but it will not be outrageously expensive -- except in the highest grades. MS64 is the grade seen most often, and any grade above that is very rare. A single PCGS MS66+ is the best known.
The strike quality on this date is particularly strong for a New Orleans Mint product and it is certainly better than the strike quality seen on some of the preceding years. Weakness usually occurs on the denticles, which sometimes appear flat.