The Broken Room is a name coined for rooms that seemed to be broken because its name would not show in the room name. Its cause is simply word-wrapping: when a word becomes too long, it moves the entire word to the next line. The rest of the game covers the next line, and so the game simply appears to have no room name. This same effect occurs for room names in the friends list.
To many users, a broken room seemed to bring higher chances of crashing, but that was confirmed a myth. There is no difference between broken rooms and regular rooms.
To create a broken room, the room name must be a combination of letters and numbers with a cumulative width of at least 135 pixels, with no spaces. Or just enter room name in Cyrillic.
Another type of broken room, is when the name has a symbol that the game does not recognise. These symbols can be found by googling "facebook symbols". When you make a room with a letter and that symbol, the rooms shows up as /room ? and the word. No one can come in the room without the original symbol, else they go to the real room ?. These are used to create real private "password" rooms. In "password" rooms, mice can set a password and invite their friends to go in with them.