Do you feel like you know the difference between a mint error and a "damaged" coin? Do you know the difference between an error and a variety? If not, you should take the ANA's correspondence courses ""The Modern Minting Process", and "U.S. Minting Errors & Varieties." They are excellent courses which will teach you all the fundamentals (and more) about errors and varieties. You will then have a solid foundation to grow and learn as an error or variety collector.
Here is a link to the ANA's correspondence courses: https://www.money.org/diploma-program
For those of you who are not members, CONECA is the no.1 error coin club in the United States. It has approximately 650 members across the U.S. and around the world, with members participating in writing articles for the club journal "Errorscope", and with annual club meetings held in conjunction with the ANA World's Fair of Money. The club also is a excellent way to connect to the "experts" in the hobby, as well as other error coin collectors.
If you are not a member, we strongly recommend it. Here is a link for more information about the club: http://www.conecaonline.org
To join, you can sign up here: http://conecaonline.org/content/join.html
Above Image via Coin World
The Denver Mint is very concerned about catching any errors before they make it out of the Mint, as this article details. Interestingly, the Mint employs a tool for catching rotated dies, and also for checking the coin's thickness. Additionally, the article shows photos of the Mint employee visually checking coins (which is done every 15 minutes.) The odds of a cud getting out are slim.
Here is a link to the Coin World article (be sure and view the photos in the article.) http://www.coinworld.com/news/us-coins/2017/08/denver-mint-still-production-workhorse-for-circulation.html
There is a lot of talk in the last decade about "gradeflation", and it's effect on the coin market. Dealers and collectors are worried about changing standards, and the effect it has on their coins' value. It is this author's opinion that collectors need to go back to their roots, and stop collecting "grades" and instead start collecting "coins."
What does it mean to collect a "coin" as opposed to a "grade"? When you collect for the grade, you are buying primarily based on a coin's numeric coin grade; is it an "MS-64" or is it an "MS-65"? That is your concern when you grade-collect. If you are coin-collecting, you are collecting based on the rarity of the coin (e.g mintage of 200 coins vs mintage of 2,000,000), the beauty of the coin's surfaces (luster, toning, spots, etc are more important than the numeric grade), and also based on the history and story behind the coin.
Mint errors are collected based primarily on demand for the error type (which could be called the "history or story" of the coin), rarity and last of all, grade (also, grading standards for mint errors are much looser than they are for "regular" U.S. coins.) Error collectors are far more concerned about the coin, than they are about it's grade. They are much more "coin collectors" than they are "grade collectors."
This approach also makes a lot of sense for collectors who are collecting non-error U.S. coins. Within any given U.S. coin series, a coin's rarity should be the primary concern, and the "grade rarity", should not matter that much beyond perhaps 3 tiers of mintstate (MS-60, MS-65 and MS-70), with prices reasonably reflective of those grades, but not of that much concern. Things like surface quality, ugly toning/spotting, distracting marks, strike, etc should be more concerning to collectors than a numeric grade number.
Grading standards for mintstate coins are unstable and changing, and are actually very hard to even define, so why is everyone buying based on this unstable "grade system" of collecting? Rather than worrying about a coin grading MS-66 over an MS-65, buy a coin for it's physical rarity, overall pleasing appearance, and leave it at that. People seem to be "grade collecting", when they should be "coin collecting."
One of the most well known and popular U.S. mint errors just sold: a 2000 Sacagawea dollar/statehood quarter mule. The coin is graded PCGS MS-66 and brought $85,000, and was sold to well known Sacagawea mule collector Tommy Bolack, who now owns and incredible 12 examples.
Below is a link to the Coin World article.
Note: above image is courtesy of Fred Weinberg