The Internet can open your phone up to viruses if you don't have proper protection, even apple has been hit although the wont admit it. The media has already reported it a few times.
Also the screens are to small to see much on the net and if you don't watch your usage you can easily go over your data limit and it will cost a lot.
Also the phones have gps so when the phone camera is used without turning the location feature off and the picture is uploaded people on line can get the long/lat of where it was taken. Stalkers use that to find their victims. CNN had a special on that a while back.