One of the tests I used to gauge the WiFi capability for the iPad mini is how AirPlay performed when streaming video to an Apple TV. I tested the mini with a variety of apps, including the ABC Player, iTunes, NBC and others. In short, video playback was smooth and the audio was crisp.
What's interesting about using AirPlay with a mini, is that it feels like a fancy remote control that has volume adjustment and programming selection. It's much easier to carry around the living room than the full sized iPad, and definitely easier than a laptop.
On the downside, when I watched ABC Player, NBC, and WatchESPN, the video was not full screen on the HDTV. It's kind of a letterbox look. The good news is that the quality was terrific.
In a sense, the iPad mini feels like a mini DVR. Choose the Apps you want and connect to an Apple TV over WiFi... and enjoy.