Small compact cameras suffer from shutter shock. Mirroless cameras now have solved this issue by using electronic first curtains. It is nice that Nikon makes small DSLR's like the D3300, but they should deal with this shutter shock issue.
If shutter speed is within 1/30 to 1/250, the images look slightly blurry. Not very bad, but noticeable. Because this is the mostly used shutter speed range, so you almost never get tack sharp images with D3300.
With the 18-55 VR II kit lens, these are shot at 1/15 and 1/320, respectively, and both are tack sharp:
But at 1/160, it is not as sharp as above:
Even at 1/30 and 1/250, the differences are still there:
With the 55-200 VR II kit lens, results are similar.
Tack sharp at 1/15 and 1/320:
The worst is around 1/60 - 1/80:
Compared to the 18-55, 1/250 and even 1/200 are not that bad:
As you see, the worst case is still not too bad and you may simply forget about this issue and just shoot at any shutter speed. But, if you want an image that's totally tack sharp, then avoid speeds from 1/30 to 1/250.
As long as you can avoid shutter shock, these kit lenses and D3300 produce excellent sharpness, very close to my Sony 35mm/1.8 on a5100, far beyond what an entry level kit usually suggests.
Some interesting discussions and reviews regarding shutter shock. D5300 and D5500 also have this issue.