It's not like you can say "in one second, only half a second of time passed," because that makes no sense surely...? How can you measure how fast time is passing?
Another example of time dilation is this: take two really precise clocks, carry one up a mountain and back, and compare it to the clock that stayed at sea level. The one at sea level will have run slower and be behind compared to the other clock because it spend some time in a place where gravity was less.
Here is a guy that did exactly that in 2005 on a tour using his van. He even took his kids: http://www.leapsecond.com/great2005/tour/
after 6 months on the International Space Station (ISS), orbiting Earth at a speed of about 7,700 m/s, an astronaut would have aged about 0.005 seconds less than those on Earth.
And then also, does the velocity have to be constant in some direction? i mean what if you're moving back and forth one inch at the speed of light, would time still be slowed for you? what if you're moving back and forth one micron?
And yes even if you were moving back and forth by one micron at close to the speed of light then an observer stationary relative to you would see your clock tick slower