From another ESL teacher aks vs ask is a dialect difference.
It's incorrect in British English or standard American English to say aks. That doesn't mean aks is always incorrect - it's perfectly correct in the dialects that use it which I believe are Caribbean/Jamaican. If somebody has roots or exposure to these dialects then it might be perfectly fine for them to say it. Your average white teenager who grew up in Coventry is probably being lazy, and it is fair to correct that usage.
In American English it is considered very bad grammar to say "He has got a pencil" whereas this is taught as correct in many ESL textbooks which originate in British English, and indeed, the "has got" form is the dominant one here. (We normally shorten the auxiliary have so he's got a pencil, she's got three sisters, etc). This surprises American expats when their children begin learning ESL in European schools.
Pedantry of an ESL nature has to differ from pedantry of a native grammar teacher nature because your points are different. Students of ESL need to understand various dialects which means listening to the differences between them, and most people will struggle with sounds in a foreign language which don't exist in their own. For example, many English learners find the th sound difficult and substitute t, d, s or z. This isn't necessarily incorrect - native Irish speakers of English don't pronounce th like the English or Americans do. Somebody's accent and dialect can be a huge part of their identity. I don't think most Brits would be impressed if they were suddenly asked to speak American English all the time just because it's the most widely-spoken variety of English in the world. Even within British English there is not complete standardisation. Bath and bah-th, up and oop, the Scottish rolled R and the invisible non-rhotic R in girl, for example.