Well, you'd have to open the port on your firewall for MySQL (if you don't already have it open) which makes it at risk of DoS/DDoS attack... unless you make it so that only one IP of the user that needs to access your MySQL remotely can pass through the firewall on that port. If the user is trustworthy and you are sure of what they are using it for, there wouldn't be a problem/security issue in allowing one specific IP through to it (unless that IP gets hacked).
Opening the remote access to the server for the whole world using wildcard is not good. You can give remote access to specific IPs. This will make sure that only those specific IPs can access through mysql port.
Just as everyone else has said, Just allow the specific IP's that you want to access it through your firewall. Opening it to the general public can cause some serious issues if people decide they want to mess with you (which will happen)
You should try to secure your mysql password and check the permissions of the configuration files it should be 600. Also mysql comes with the different logs files you should keep track of client connections, queries and server errors.
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You can allow IP based MySQL connections to outside world but still you have problems if the client files have improper permissions or poor coding. An attacker can inject your whole server's index pages.
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