1. Career progression, especially in management is limited. You will be much better off career-wise in a company that supports and lives remote work than in the one which simply allows it.
2. Some people say it's difficult to negotiate salary increases, which is true, but not unlike negotiating anything else without personal presence. So make sure you negotiate during your regular on-site visits.
3. On-site visits - those really important for many reasons. You may like where you are, but even if the company is fully remote you still need to meet all the folks every now and then. That's in our human nature. However, this is a problem - you need to figure out of often, where to stay etc. Organising getaways with your team requires extra effort from your manager.
4. Meeting participation is difficult. You must overcome the rudeness of interruption. With the network lag you will most likely have to interrupt other people all the time in order to be heard. Also, since you can't just draw on the board easily, so make sure you're well equipped with tools to run your meetings. Take notes, close all irrelevant windows and participate fully.
5. Most managers want an easy life. If you are remote and they aren't, they need to put extra effort to support you. This is even worse if you are the manager or team leader yourself. That means they would often press for reduction in the remote work, so it's easier for them. It would require you to not only prove your worth, as in any workplace you want to grow, but also prove the remote work's worth. Unless there are many more people and the company sees the benefits and opportunities of remote work, it will drain you fast.
6. When it comes to payment that is usually quite easy, especially in the EU - a simple bank transfer. The taxing can be more tricky, but there are four most common options here: A) contracting agreement / self-employment / invoicing, B) having your employer to set up an office in your country, C) performing the duties of the employer of their behalf by yourself in your country, D) being sent for delegation, and regularly renewing it. If you're in EU that may give you tax benefits, if you live in a lower tax country than your employer is, and there is a decent agreement between those two countries to avoid double taxation. If you're an USA citizen though you'll probably not going to like having to pay double taxes. Please seek advice on that one.
7. Health care / insurance - in the EU you're usually better off not taking the company-offered insurance, but relying on the public health-care entirely and just paying for private visits out of pocket. If you like extra treatment you can get a private insurance, but it pays off in very few countries and situations. For the average person the health care in the EU is not that expensive, outside of what you're paying in taxes.
8. Not moving much. This is a big one, especially if you're working remotely from your home. You need to exercise a lot and go out as much as you can.
9. Educating people around you that remote work is still work. Your partner, children, parents, friends. Many of them will not understand at first that even though you're at home, you're actually working. On top of that, if you're taking a break, that is not to help out with some chores or other gardening tasks. It's the time you take to clear your brain, relax and get back to work afterwards - as if you were in the office. You wouldn't be asked to take the trash out while you went for a break out the office, would you? So, just find an agreement with your cohabitants - they will easily understand that once you explain it.
10. Isolation. The lack of personal contact with your peers can really hit you. Make sure you meet with your local friends regularly. Ideally the people you can laugh with and those you can talk to more seriously. Also, try to inject random topics when calling your workmates, maybe when the meeting is over early. They will appreciate that, and so will you.
There is a lot more to sort out, but the possible benefits of the remote work are fantastic. Enjoy!