When does a mistake become standard usage?

It depends on how useful a hole in the language the neologism is filling. If something becomes urgent as a topic of conversation and there was no word before, then it can quickly be accepted.

If a word is misspelled, people are more likely to resist the change, especially if the the old spelling is deeply entrenched, and it can take many years for the change to be accepted. It tends to go by critical mass; when enough 'respected' sources use a word - which used to mean broadsheet newspapers or literary magazines or novels or other books - then the lexicographers would pick it up and add it to the dictionaries, and the word would start to be accepted.

In the internet age, the process takes place much more rapidly. 'Weblog' gave way to 'blog' in almost no time at all.

A silly answer although it's probably true: "When Google returns meaningful results without suggesting an alternative spelling"

That's an interesting question, but it doesn't really have a well-defined answer. The useless but essentially correct answer is "when enough people think it's correct".

The thing is that, no matter how hard people try to argue otherwise, prescriptivism doesn't really work that well. Language changes are slow and amorphous, so it's hard to draw a definitive line in the sand where something goes from right to wrong. You can probably find points in time where it's pretty clear-cut if it's one or the other, but there's no exact point in time where it makes the transition.

It depends how common the word is.

A very obscure technical term may only get a handful of mentions in print by a couple of authors so it's very easy to change - while a common word will remain unchanged for centuries.

The most famous recent one is "a flange of baboons" made up for the Gerald the Gorilla sketch on "not the nine O clock news" which made it in the OED "askoxford" site and is now used in scientific literature