To report an offensive message sent using My Messages, click on the red flag on the top right of the message.
The kind of issues that should be reported are scams, where a Habbo is asking for your password in return for Credits, scam websites adverts, swearing and inappropriate behaviour.
Please do not report Habbos just because you had a falling out with them. It's better to just remove their names from your console and ignore them. Only report genuine messages, as you will be taking valuable time away from Habbos who really need help.

'My Messages' is a Habbo email-like messenger. It allows you to stay in touch with your Habbo friends easily, even when they are offline.
You can send messages to your friends with links to group pages, rooms or other Habbos' home pages. If a friend is not online when you're in Habbo, remember to send a message, and the next time they log in to Habbo, it'll be one of the first things they see.

'My Messages' is located on your /me page, just underneath your Habbo status box. To get to your /me page, click on the tab with your name, or 'Home', from any Habbo webpage.
If you have new messages, the Friends List icon on your Habbo toolbar will have a ! on it. When you open your Friends List, you'll also see a flashing yellow envelope to tell you you've got mail.

Much the same way as any other email program you may have used. You can compose messages, send them, check received messages, delete messages and organise messages. You can only send and receive messages from Habbos that are on your friend list but they don't have to be online. When you delete messages, they'll show up in your Trash.

You can only send 'My Messages' to Habbos that are on your friend list. Add the Habbo to your friend list first. Then try sending them a message.

Maybe you're trying to send messages too quickly. Just wait for a while and you'll be able to send another message.