the 50Mb is the speed you are connecting to the outside world, doesn't affect anything that travels on your internal network.
how are you playing?
that requires an excellent network connection to work well, and even then will probably have a bit of jerkiness
You'll want to hard wire one, probably both, of your laptop and the TV to even think about using mirroring.
Mirroring does work well for things where the whole screen isn't constantly changing like it does in a movie.
to get better results than mirroring, look at beamer.
mirroring has to convert your screen in real time, it doesn't know what's going to happen on the screen till it hits the screen. plus it has to keep the 2 monitors in sync, so it sacrifices some quality for speed.
Beamer is able to read the actual file and get ahead a bit.
How far away is the Wireless Router from the AppleTV and the MBA, this can also play a big part is your streaming experience.
Actually many variables can play a part in wifi streaming which is why I hardwire everything that can be connected to ethernet.
The antenna wifi power output, distance from computer to router and from router back to aTV, the WiFi channel used on the router, walls, material of walls, insulation, etc can all play a part in your wifi experience.
I noticed some issues with streaming Sling TV from my MacBook Air. I think I just noticed it on the ESPN channels, but it's like the framerate drops by about 50 percent. Could be a programming bug since the iPad streaming works fine. Just makes me wish Sling could get an app made for Apple TV in a hurry.
when streaming from the air using mirroring, it's going to be jerky and missing frames, mirroring basically sets up a virtual camera inside the video card and records the screen image, then converts and streams it in real time, it sacrifices quality (and frames) to maintain sync between your computer monitor and the remote TV screen. and also because it's a quick encode, it's also not as optimized as it can be, so it will be a larger file.
when airplaying from your ipad, it takes a pre-encoded stream and forwards that file directly to the aTV (or tells the aTV where to find the stream on the web, and then the aTV will download it directly)
if you're watching a digital stream on the web, even if it's "live" they'll take an extra bit of time to process a good stream, maybe only a 1/2 second, but it's enough to get a better quality. but that would be enough to annoy the crap out of you if you were watching 2 screens beside each other like you do with airplay.
If you were to compare a digital cable box, analog cable into the tv, a live web-stream and an antenna pulling the signal off the air of the exact same broadcast, you would find vastly different timing in when it hits the screen.