Given a certain U.S. coin, year, and mint mark, how can you find out what the highest graded specimens are? Edit: PCGS Population Report and NGC Census Report?
Yes the population/census reports should give you the info. One can also get to the same place by entering the cert number of any coin (you might have or find online) on the cert lookup tool and then clicking on one of the links that takes you to population info.
Can you just add the population numbers for PCGS and NGC (exclude the others for simplicity) and get accurate totals ? With all the crossovers, how do you know if there's double-counting or not ?
You don't. The populations are good for knowing relatively how many of each is graded. However, the crossovers and crackouts make numbers inaccurate. For some coins (say an 1881-S MS 63 Morgan) it doesn't matter too much as we know already that there are a ton of those coins. However, some coins are seriously skewed. For example, a single coin might have been sent in 10 times with 9 MS 66 and 1 MS 67 result. This would move the MS 66 population up by 9 when there really aren't 9 new MS 66s.