D3200 Video Codec and blown reds
It's likely just like the earlier bodies, which means the video clips will look exactly like out-of-camera jpegs would.
If the 3200 allows exposure fine tuning like the 7000 does, bring it down a notch. This will help stills, too.
And most importantly, videos will have the exact look of your selected Picture Control. Neutral looks like crap by default, but it's the preferred look in videography - you just grade it in post to your liking. You can also install one or more of many awesome custom picture controls made specificaly for movie making.
I have a "Kodak Kodachrome" one which I enjoy very much, it's nice and contrasty without subdued saturation and it doesn't easily blow out highlights or reds.
The "Ektachrome" look is a lot more extreme, low saturation but very high contrast. Makes skin look gritty and detailed.
There's a lot of space to play around in video mode, the "standard" picture control at default exposure is far from best.