It is possible to record rare features of a language because it is possible to encounter such a feature, and it is possible to record. It is up to the linguist to take appropriate note of the feature, which does depend on the background and interest of the linguist. Even a native speaker of a language may be completely unaware that his language has such-and-such feature, in fact it is uncommon for native speaker linguists to initially have awareness of "rare" features of their language which are not also found in the dominant standard language(s) of the region. Outside of certain parts of Asia, tone is an "exotic" feature of language not found in standard languages, but tone is overall not a rare feature in language (between 1/3 and 1/2 of languages have tone). Commonly, linguists who are starting their training, and speak a tonal language, will "miss" the fact that tone is a significant feature of their language.
There is a continuum of "not getting" some feature of a language. One end is absolute unawareness. Staying with a theme, the linguist could be completely unaware that the language he is looking at is tonal. There are various linguistic reason for this unawareness, such as that tonal distinctions have very low functional utility especially no grammatical distinctiveness, or it has low physical differentiability (differences in the 5-10 hz realm; very long spans for physical realization). The linguist can contribute to total unawareness in unnummerable ways, for example they only worked on the language for two weeks; they gathered the wrong kinds of materials (raw conversations between speakers); they didn't care enough (put differently, the linguist is focusing on something else: looking at pragmatics, not phonemes; looking at phonemes, not information structure encoded in tenses).
The way that we discover rare features is that we pay attention and return to things that are puzzling. We can do this if we are engaged in a long-term controlled scientific investigation of the language. Even if we weren't carefully trained to transcribe tone, fancy duration properties or distinctive vowel phonation, we are capable of noticing that some two words have similar yet somehow different vowels. When you notice such a thing, you start to wonder "Hmmm I wonder if there's some distinction in the language that I'm not getting", so we dig deeper and eventually we learn that breathiness is contrastive, that there are 4 tone levels, 5 types of falling tone, or three degrees of length. With more and more experience, you better able to notice obscure things about new languages.
That is ideally. In reality, sometimes we don't notice at all, or we notice something yet can't figure out what it is or how to notate it (some people say they are "tone-deaf", which is not ever true, but some people are really bad at it). We may not really care enough about the feature to ask all of the relevant questions (semanticists typically don't mess with transcribing tone; phonologists typically don't mess with the elaborate contexts required for distinguishing kinds of focus in verbs). We are not all in it for the really long-haul (decades of research on a language). Sometimes we don't record everything, so if you made an error in the field, you can't go back to the recording and re-check.
I don't think it's possible to say anything substantive about rates of blatant error in fieldwork. Very rarely, we can know that X is wrong about some language that they were working on; more often, we know that we found something different with our speakers, but here are dialects, and languages change. We do know, though, that there are very few absolutely perfect descriptions of languages: we don't expect a description of a language to give an absolutely flawless description of word order, morphology, semantics and phonology in some language.
Field workers don't actually get much by way of training in what exists in languages. We get a relatively standard superficial exposure to unusual sounds in the general phonetics class (which usually amounts to learning IPA for English then maybe a week of "not English" sounds and symbols); other general linguistics classes don't provide you with the cross-linguistic background needed to immediately recognize "Aha, this is an ergative language!". What we get in field methods training is experience in figuring out how to collect and make sense of data. So "what is known" in linguistics doesn't have much applicability to the average field linguist. There are some institutional exceptions, where students have extensive and relatively rigorous training in grammatical diversity.