One of our responsibilties as a work of mercy is to admonish the sinner and rebuke sin. I get that with those closest to you, we are to handle it with love and only rebuke if it is a last resort. On the other hand, given that sin runs rampant in the modern world, how are we to deal with the sins of others? Are we to admonish everyone we meet, and if so, is it for every single sin or only mortal sins, etc.?
We are to handle everything with love. Not only what relates to those closest to us.
In my experience, we don’t have to seek out opportunity for admonishment. It’ll find us.
And the admonishments we’re most immediately called to give are often far more uncomfortable and inconvenient than some distant admonishment of a stranger you might be thinking of. The closer the log is to our own eye, the more relevant it is for us to address it.
E.g. you’re likely to hear gossip from someone who likes you and trusts you enough to gossip to you. So it’s someone close to you that you have to (lovingly) admonish on that front.
Regarding whether to help someone grow out of just mortal sins or venial sins: well, how much do you love them? Enough to only want them to be free from one, or both?
Keep in mind that the purpose of educating someone about right and wrong, is to help them grow towards what is right, because it is good for them (and for everyone). What it looks like to
effectively educate a given individual about right and wrong on a specific topic, will vary. And may take time and patience and lots of support beyond some simple “By the way that’s a sin” (though there’s a time and place for such simple alerts). And there’s an order of priority, certainly, in terms of which challenges we help people tackle first. Mortal sin being more crucial than venial, though venial still being important to help each other out of (not least because habitual venial sin tends to lead us back to mortal sin).