So you've got a serial misspeller in the office. What you can or should do about it depends on who the culprit is and your relation to them.
Not your job. Correct him in the moment if it could cause issues externally but otherwise assume that his manager is handling it or doesn't consider it a problem.
I’d say you shouldn’t say anything. Presumably he also does this around his manager, and it’s that person’s job to address it. For your own sake, I’d skip creating the awkwardness that could result if you tackle this yourself.
Source: should I correct my boss’s awful grammar?, Alison Green, AskAManager
It depends on how long you've been at the company, how new the coworker is and how long the problem has been going on. If you're new to the team, don't mention it as it just won't look good even if you mean it well.
Otherwise, you could offer to help out or bring it up if you've got a good relationship with the coworker and can do so tactfully. But really, this is also not your problem: it's up to your coworker's manager to control the quality of her work.
Bring it up with your manager if it's affecting clients, external communications or your work. Otherwise, assume that your manager will address it in time or doesn't care.
It’s not really your place to speak up about it. As you point out, his manager sees the same things you do, and it’s up to her to address it. If she’s not doing it, then it tells you something about what her standards are, which tells you something what kind of manager she is... which actually points to the bigger problem being with her than with him.
Of course, it’s also possible that she is addressing it with him. That’s not something you’d typically know about, since managers don’t generally broadcast to the rest of the staff when they’re having serious conversations with someone and issuing warnings. Once the behavior has gone on for a certain amount of time with no change, it’s safer to assume that nothing is being done — but even then, different workplaces take different lengths of time in addressing these things.
Source: should I speak up about my coworker’s lack of professionalism?, Alison Green, AskAManager
Whatever you do, don't be this person and start whistle-blowing individual mistakes to management.
Someone you manage
If there's a pattern of spelling errors then it's worth addressing. Addressing each individual instance won't solve the underlying problem.
This is the step that managers often miss when they have concerns about someone’s work — they continue addressing each instance of the problem, and they get increasingly frustrated and concerned about the pattern, but they don’t sit down with the person and say, “Hey, we have a pattern here.” They assume the person sees the pattern as clearly as they do, but they never spell it out. But you need to spell it out, because your employee may not see it as a pattern or realize that it’s risen to the level of a serious concern.
Source: my employees are making mistakes, but I don’t want to micromanage, Alison Green, AskAManager
How much effort you and the employee should make towards proper spelling and grammar depends on whether her mistakes are visible externally which could mean to clients, the public or other departments. If the mistakes are affecting his work, you should treat it as any other performance problem.
In most cases this is simply the result of lazy writing or a poor grasp of grammar and spelling. Both causes are fairly easily remedied if your support your employee and give her enough time and resources to improve.
And I’d also like to see you be more vigilant about using correct grammar, in order to present a more professional image to the people we work with. You have lots of potential here, but this is something we need to work on fixing because it’s something that could keep you from accomplishing all you otherwise could.”
Sending her to a business writing class could help things.
I don’t think you need to worry about this being snooty unless you’re secretly feeling snooty about it (in which case it may come across). Instead, you should see this as feedback like any other, and simply be straightforward and direct in giving it.
Source: helping an employee with bad communication skills, Alison Green, AskAManager