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As coin collectors how important is it to know exactly how coins are made or the history of specific coins, or any other technical or factual information?
It all depends on how deeply you want to get into numismatics. If all you want to do is buy a coin and fill the empty hole in your folder, the only thing you need to memorize is what series you are working on. Why memorize what you have or need? They keep changing, so carry a list. And yes even if you do want to know more you could keep books around and look everything up, but if you are always looking up the same thing over and over again you one aren't learning anything, and two are wasting time.
As mentioned a good knowledge of how coins are made assists in the identification of varieties and errors, and also in recognizing counterfeits and pieces that are being sold as errors but which are really post mint damage.
The more knowledge, historical and technical, that you nave the more interesting things become and you start seeing connections and interrelationships between coins, people, events, history, etc. None of this is available to you if you have to look everything up.
It is also easier to be mislead if someone offers you something or you think you may have found something good, but you don't have your reference materials with you so you can look things up.
In short, more knowledge is always better than less knowledge, and the simple acquisition of knowledge came be enjoyable in its own right. Sure there are some things that DON'T need to be memorized, but there are ton of things that are fun and useful if they are committed to memory.