Ok, these are things that really annoy me when I see them. Not in those for whom English is not their primary language - but in my fellow Australians, Americans and English people. Especially as for some reason they are seen more commonly in those I know for whom English is not only a first language, but usually the only language than in those I know from other countries (who commonly speak at least two other languages)!:
your/you're - the 'your' is so often misused, as in 'your the best' or 'your so stupid'. It is not hard, people. If you would say 'you are' then you're should be used: 'You are the best' = 'You're the best' etc. Just think about it. Each time you are going to type your/you're, think 'could I be saying 'you are'. I learnt this in year 1. Apparently a lot who went through the same education system didn't manage to. Here is a wikihow article on how to use them correctly.
cat's/cats - if you are referring to more than one cat, as opposed to something the cat owns, there is no apostrophe needed. So correct is 'the cat's bowl'. Incorrect is 'look at all those cat's' - it should be 'look at all those cats'. And the shop by my train station should certainly be selling sofas, not sofa's.Just remember, if adding the s to indicate more than one, no apostrophe needed. Easy, right?! Wikihow explain this nicely...just in case you need reinforcement...
hay/hey - I have a friend who says 'hay' rather than 'hey' as a greeting. I have told him to use 'hey' over a year back but he continues to 'hay' not just me, but others I have seen him chat to/email.
awe/aww - Awe is a feeling, aww is what we say to something cute/sad etc.
come/came - People using 'come' when referring to past tense. Saying 'I come back home at 9' rather than 'I came back home at 9'.
anyways - It is simply not a word. Don't use it.
there/their/they're - Use incorrectly so often (along with the to/too) that I will not even comment. Except to say, read something about it! Wikihow again on to/too and there/their/they're.
lose/loose - You lose a game, your clothes may become loose if you lose weight. Get it! (photo showing this is from the BBC website - there because this is such a problem in the UK).
Of course, it is who the perpetrator is that determines the annoyance factor. Not at all annoying in children, those for whom English is a second language or the dyslexic etc. Very annoying in those who should know better, and especially in those who are higher status at work. Not annoying on chat if clearly from haste rather than ignorance. Annoying in official signs and documents. See, I am not unreasonably grumpy. I am reasonably grumpy. I am.