My co-worker and I started at the same time, mid-summer, so we each have 9 days of vacation time through the end of the year. Our new boss works remotely and there is very little accountability. My co-worker has started missing a lot of work lately. Sometimes he'll email the team and give some medical excuse (sometimes telling me a different excuse--like just being tired or out with friends), but most of the time, he doesn't send out an email at all, just hopes nobody notices. He's up to 23 days off, but he's not reporting all those days. I talked to my manager about it a couple weeks ago and he said that he was trying to give leniency to this employee because of his medical issues, because he doesn't know that they aren't as valid as he thinks. I feel like I've done all I can do by talking to the manager about it, but it's getting out of hand. He hasn't been to work in a couple weeks, and my manager doesn't seem to care at all. Is there anything else I can do about it?
I talked to my manager about it a couple weeks ago and he said that he was trying to give leniency to this employee because of his medical issues
That obviously is your first step and you've done it. You're not a manager and more specifically, you're not his manager. For you to do more would be stepping on your manager's toes, big time.
I feel like I've done all I can do by talking to the manager about it, but it's getting out of hand.
You're right, you have done all you can do since that's really the only thing you should do. So having said that, they only thing you have left that you can actually do is approach your manager one more time and let him know the specifics of your concerns. Be aware though that this may annoy your manager and may backfire, but if you're determined to do something, there's really not much else you should do. Anything more than this (such as going over his head) could well up with you ending up looking like a great big troublemaker, and looking worse than your coworker, possibly even looking jealous because he's "getting away" with something.
If you do decide to approach your manager, I'd start out by saying that you feel really strongly about it and felt you had to say something else but that this is the last you'll say on the subject.
Think about what you're saying though and be careful. You're essentially saying that you're manager is incompetent and that you would be a better manager than he is because you would handle it. If we can make that assessment, I'm sure your manager will too.
Tread very lightly.
If you feel that you still need to approach your boss about this, then you need to talk about how this is affecting you. Is the absence of your coworker making it difficult for you to do your own work? How is this impacting the team and project? Don't say that the coworker needs to be punished or investigated - just talk about how to improve your ability to do your job. This might mean redistributing your coworker's tasks, or maybe hiring someone to fill in the gaps. If your boss determines that your coworker needs to come into the office more, then that is management's decision, not yours.
If your coworker's absence is not affecting your work, and really just bothers you for the principle of it, then let it go. You have alerted management that there might be something up, and you are still able to do your job, so the ball isn't in your court anymore.