When you're talking about WiFi, are you talking while streaming locally or remotely? If know the answer might seems obvious, but sometimes people connect into their neighbor's WiFi and think its local. The other question is if this is happening on your computer as well?
As for mobile broadband (3G/EV) that's usually port forwarding issue. Once you've setup the Slingbox for viewing locally, its the routers responsibility to allow remote viewing. I recommend that check your router's firewall rules. You'll need to make sure that that the corresponding public UDP and TCP ports and being forwarded to your Slingbox's private IP address. Most of the time this problem is associated by only having the TCP port forwarded.
IP address and Port Number: http://support.slingbox.com/get/KB-005866.html
Port Forwarding: http://support.slingbox.com/get/KB-2000068.html
Network Setup Assistant: http://support.slingbox.com/get/network-assistant.html
Manual Changes: http://support.slingbox.com/get/KB-5000126.html
Before I corrected the problem, my Slingbox itself started malfunctioning. According to what I have read, it appears the AC adapter is the problem, even though it checks out OK on a meter (inexpensive meter). I am trying to find a matching adapter but am having a hard time getting a perfect match. I will respond to the Hero question when and if I get the darn Slingbox working. I have used the Slingbox and the HTC app for a total of just a few hours. This is getting to be an expensive luxury!