Basic question about sockets and security

[Dave Dean]

Hi all,
  I'm just starting out in sockets/network programming, and I have a very 
basic question...what are the 'security' implications of opening up a 
socket?  For example, suppose I've written a simple chat server and chat 
client.  The server opens a socket, listens on a port, and accepts incoming 
connections.  The clients open a socket and connect to the server.  If the 
server receives a message from a client, it sends that message out to every 
client.  When a client receives a message, it places it in a text widget.
  So...are there inherent dangers in doing this?  I have no real security 
concern in the actual application, but can an open socket somehow allow 
someone access to the rest of the computer?  Is the 'security' of the socket 
handled at the OS level (or within the socket module)?
  I realize this isn't necessarily a Python question, but I wrote my 
application in Python and I'm not sure where to start.  I'll repost this 
elsewhere if someone points me towards a more relevant group.
Thanks,
Dave