What @
EJCC said captures most of it I would think, but there are a few areas I don't quite agree (largely through observation/experience).
For NTJ's: They definitely do hide their idealism better than other 1's. To the vast majority of them, one if their morals/ideals is to
not display said idealism. 1's in general can get pretty meta with their personal rules, but I think NTJ's take the cake in that department. You'd think they'd be some of the coldest and unfeeling of the NTJ's, but 1's in general have a poor reputation for being cold. Externally, oh sure they very well will be. Internally? HA! 1's feel all kinds of crap, and NTJ 1's are no exception to this. They aren't going to show it though unless they have been given a reason. Unfortunately, that reason is usually for bad stuff (hence the villain suggestions are apt here). I see more INTJ 1's than I do of ENTJ 1's, but I do know at least 1 of each. In both cases, they're pretty controlled of themselves most of the time, but there is this under layer of warmth that doesn't stay completely hidden (much to their chagrin a lot of the time). Since 1's integrate to 7, nearly all of them of all types have a "silly switch", and NTJ's are no exception. It's quite a sight to see

. The anger in NTJ 1's tends to be the most destructive, but the most infrequent. When it does comes out, they will
burn everything.
For NFJ's: It's sort of the opposite of NTJ's, where they have an underlayer of warmth, NFJ 1's have an overlayer of cold and occasionally a cold core. Generally, NFJ's are regarded as positive lights much of the time, but it's very easy miss an NFJ 1 for some other type combination. Reason being is on the surface 1 and NFJ run in opposite directions of each other. However, in those individuals, there is consistently a moral ideal system that is VERY strict for them, yet it's kinda fuzzy. They sort of "make it work", and when you get to know one, it does become apparent there is a lot of logic and fairness to their rules. It lacks the structural rigidity of T's, but is generally much more stubborn and strict overall because they can (and readily will) create unseen logic turns to fit their code. Their idealism often appears very... sad from the outside? It also tends to swing from extreme good, to extreme bad. NFJ 1's have a terrible case of black and white thinking. Perhaps more than SJ's which are often said to have that the most. Make no mistake though, it's idealism through and through. The anger in NFJ 1's also tends to be the most extreme and visible, and frequently self-destructive in process. If you've ever watched Adventure Time, a really good example of an ENFJ 1 is Princess Bubblegum.
For STJ's: They're your "classic 1" in the sense that the structure of an STJ's mind, and what a 1 is tends to align fairly readily. They win in the organization, completeness, follow through, and reliability department hands down. Those things tend to (and often are) absent in N 1's. STJ 1's tend to want to be much more externally ordered, which is why they come across as so well put together. Much of the time it's a show. Similar to NTJ 1's, they generally loathe to show weakness or disorder. They want to be seen as externally perfect, and are the most sensitive to this image. Almost every STJ 1 I have come across has a strong 3 fix (where as the other types tend to lack a fix pattern from what I noticed), and care immensely on how they come across. However, it's all in accordance with their morals and code. You can meet STJ 1's who are incredibly rude blunt or aggressive, which doesn't suggest 1. However, it's often that rudeness isn't seen as important to their code, and other stuff is. This is IMO, the primary reason why STJ 1's will mistype as 8's (which is rather frequent from what I can tell).
I've never seen an NFP 1. In fact, the only P 1 I have ever come across is [MENTION=1449]Magic Poriferan[/MENTION]. I don't thin I have ever come across one IRL. I'm sure they exist, but for the most part P 1's really don't make sense, and you're mostly likely to find one in the NTP form.
One of the key ways to identify a 1, is to get them talking about their personal rules or larger issues. If they can run sort of ad nauseam about them, or go on and on about "this is how stuff SHOULD be", then you likely have a 1 on your hands. The introverts are less likely to do it, but they will if they are in the right situation.