Since the most important thing to your Internet business is the address that you have your web site(s) at, you need to know that the web hosting company that has your files is going to be as secure as it can be.
The main problems with shared hosting, from a purely security minded standpoint, is that someone else on your server can do something that will cause the server to, possibly, slow down or it may even drop off line altogether. This can be done because of the programs or some of the scripts that that client has installed have been installed wrong or in just the wrong way.
This happens every once in a while and can be a problem if you are trying to launch a new product or attempting to run something that, in and of itself, might be a little edgy.
That is really the main problem with the shared way of hosting your web presence, however, it rarely happens and when it does, you usually are back up within a very short time.