It's right if other people who speak your dialect (other people in your speech community) also say the same thing systematically. In the Japanese case, it's clear that the construction is correct in his dialect, since he's not alone in using that construction. What's wrong when it comes to spoken language is usually when you make mistakes likes slip of the tongue, e.g.:
(1) a. Spoonerism: You hissed all my mystery lectures. (Intended: You missed all my history lectures.)
b. One of the lecturers are very nice. (Intended: One of the lecturers is very nice.)
People utter stuff like (1), but they do so because of memory limitations or other cognitive quirks.
(There could also be other reasons why you make mistakes - perhaps you just imperfectly acquired then language when you grew up, so you say e.g. 'deers' when everyone else says 'deer' - but that is unlikely.)
When you say something that merely deviates from the standard variety of the language, as codified in the Japanese dictionary, it doesn't mean that you're wrong. It merely means that you're speaking something other than the standard variety. Sometimes, this can be because the dialect you speak is innovative - which implies language evolution - and other times, this can be because the standard variety is more innovative. For example, it is non-standard in modern Chinese to use the morpheme corresponding to the character 至 to indicate superlatives, but it was not in Old Chinese.
A good essay on these matters is this paper by Geoff Pullum, if you're interested in some further reading.
Cases like 'you're/your' and 'alot' are orthographic errors, not grammatical ones, and are quite different from the Japanese case. Of course, with orthography there are also standard and non-standard varieties and both can also change through time, but it's not as systematic as spoken language. Whether writing 'alot' is wrong is more of a matter of definition here, though I'd say that if you're writing something that should follow standard orthographic conventions but you do not follow them, then you're 'wrong'.