As we have already explained to some extent, there are quite a lot of minor caveats with using NAT. The main problem is certain protocols and applications which may not work at all. Hopefully, these applications are not too common in the networks that you administer, and in such case, it should cause no huge problems.
The second and smaller problem is applications and protocols which will only work partially. These protocols are more common than the ones that will not work at all, which is quite unfortunate, but there isn't very much we can do about it as it seems. If complex protocols continue to be built, this is a problem we will have to continue living with. Especially if the protocols aren't standardized.
The third, and largest problem, in my point of view, is the fact that the user who sits behind a NAT server to get out on the internet will not be able to run his own server. It could be done, of course, but it takes a lot more time and work to set this up. In companies, this is probably preferred over having tons of servers run by different employees that are reachable from the Internet, without any supervision. However, when it comes to home users, this should be avoided to the very last. You should never as an Internet service provider NAT your customers from a private IP range to a public IP. It will cause you more trouble than it is worth having to deal with, and there will always be one or another client which will want this or that protocol to work flawlessly. When it doesn't, you will be called down upon.
As one last note on the caveats of NAT, it should be mentioned that NAT is actually just a hack more or less. NAT was a solution that was worked out while the IANA and other organisations noted that the Internet grew exponentially, and that the IP addresses would soon be in shortage. NAT was and is a short term solution to the problem of the IPv4 (Yes, IP which we have talked about before is a short version of IPv4 which stands for Internet Protocol version 4). The long term solution to the IPv4 address shortage is the IPv6 protocol, which also solves a ton of other problems. IPv6 has 128 bits assigned to their addresses, while IPv4 only have 32 bits used for IP addresses. This is an incredible increase in address space. It may seem like ridiculous to have enough IP addresses to set one IP address for every atom in our planet, but on the other hand, noone expected the IPv4 address range to be too small either.