I think it really depends on the person in question.
If you had to pin the new employee down, how would you describe their personality? (This is essential for managers and such who care about employees and how best to handle them).
It's rather rudimentary, but these guys have a free explanation of personalities and hence it may help you get an idea about this new employee and how to tackle your issue (this works with everyone, your boss, your friends, family), https://www.16personalities.com/articles/our-theory
Now, it's your choice to decide. Are they introverted and turbulent? Do you think they'll worry that everyone thinks they're bad at their job? Send the message, make it as friendly and welcoming as possible, the new employee will likely be looking for someone for support, to be friends with, and may come to you hopefully with any queries in the future they might be unsure about.
Are they extraverted and assertive? Do they come across as 'I don't mind making mistakes, we all do'? If so, then you'll be doing them no favours pointing their mistakes, they'll be standoff-ish and probably wont want to hear it, leave that to your manage.
I only come to mention two personality types as they're the easy ones to spot from a distance, you can usually tell if a person is happy to talk to others or isn't, avoiding eye contact and such, and you can normally tell if someone is assertive or turbulent, just by the amount they smile or frown at work.
I agree with the rest, if you're just pointing it out for the sake of pointing out, don't bother, if you're doing it out of concern for the person, then read above.