As a general rule, a "fake error" is a coin that has been either accidentally or deliberately damaged in such a way that someone might conceivably confuse it with an actual mint error. Typically, this involves mangling or mutilating the coin in some fashion.
A very typical example would be what are commonly known as a "vise job". To make a vise job, simply take a stack of several coins and squeeze them together - by putting the stack in a vise and turning the handle really really tight, or simply by putting them underneath a heavy piece of furniture and leaving it there for several decades. The coins in the stack will get squeezed into each other, and will likely leave partial impressions of each other behind. vise jobs are often mis-identified as "double struck" or sometimes as "partial brockages".
Here's a recent vise job thread. Whereas
this is what an actual "double struck" coin might look like.
How to tell them apart? Well, what really helps is to become very familiar with how coins are actually made. Once you've got a good idea on how this happens, then whenever you find an "odd-looking" coin, try and imagine some way by which that kind of appearance can be caused by the normal functioning or a predictable malfunction of mint machinery. If you cannot, then the answer is almost certainly "because it's not actually a mint error". Coin production isn't a terribly convoluted or complex process, and there are only a small number of ways that it can go wrong and create an error. There are far, far more ways that a coin can become damaged or mutilated after it leaves the mint.
Some general rules of thumb to keep in mind:
- Mint errors are valuable because they are rare. The vast majority of "odd-looking coins" are odd-looking because they've become damaged, corroded or otherwise mistreated after they left the mint. Such coins might "look cool" but have zero collector interest and value. In extreme cases, the coins have been reduced to scrap metal value as they are no longer considered legal tender.
- Use Occam's Razor: "the simplest explanation is the most probable explanation". Don't build up some crazy story about an incredibly improbable chain of events occurring within the mint to create a specific pattern of damage, when the far simpler (and therefore far more probable) explanation is "some idiot smashed this coin with a hammer". A corollary to this is "A coin very very rarely has two separate errors happening to it simultaneously". If a coin seems to have multiple weird things happen to it, try to find a single cause for all of those oddities, rather than a sequence of improbable causes.
- Be reasonable and logical. Example: suppose you find a heavily worn coin showing clear and obvious oddities. Let's be logical: if it actually came out of the mint looking like that, would hundreds or thousands of people have been given this coin in change and simply have spent it, causing the clear normal circulation wear patterns, and none of those people noticed the defect and put it aside? Occam's Razor would conclude that the coin probably did not have that damage when that wear and circulation happened to it. An important corollary to this: it's really, really hard to "prove" that a very badly worn or corroded coin has any kind of error or variety happening on it.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis