Apart from the exceedingly rare 1853-O No Arrows Half Dollar, the 1852 has the lowest mintage of any Half Dollar from the 1850's. And, it's not even close. The next rarest date is the 1855-S, then the 1852-O, then the 1857-S. . Combined, the 1852 and the 1852-O Half Dollars represent excellent values in the series because they are a fraction of the values of the 1852-O and the 1857-S when they reach the Mint State level. Thankfully, a small number of Uncirculated 1852 Half Dollars were set aside by collectors, something that is not true of the other three dates. Even so, the 1852 is by no means common in Mint State -- it is still a very scarce coin.
In looking at the images of 1852 Half Dollars certified by PCGS, it seems clear that a fully struck example may not exist. They all seem to have weakness on the eighth star, and some show weakness on most of the stars on the upper and right sides.