I'm going to assume that the problem you're referring to is the staccato appearance of the motion, i.e., it seems to move in tiny little steps rather than smoothly. The video also has very uneven panning speed because it was shot handheld, but I'm going to assume that this isn't the problem you're asking about.
This kind of staccato movement is caused by a low frame rate, typically 24 or 30fps. At these kinds of frame rates the eye can see the individual frames and so it can see that the picture "jumps" a bit between each frame rather than showing a continuous smooth movement.
This video is a bit of an extreme example of the kind of staccato movement I'm talking about, notice that you can't even read the lettering on the bus that goes by even though it's perfectly legible if you pause the video.
The best way to avoid this is to use a faster frame rate if your camera has it. For example, shooting at 60 frames per second (fps) will make this effect much less pronounced.
A warning, though - shooting at higher frame rates necessitates using faster shutter speeds, and this has two potentially negative consequences for the kind of indoor shots in your sample video. First, faster shutter speeds in indoor lighting may require you to boost the ISO sensitivity which can introduce noise. Second, faster shutter speeds may interact with lighting that flickers such as fluorescent or some LED lights to create bands of light and dark in your video, or cause the brightness of the recording to fluctuate.
If you can't use a faster frame rate, the conventional wisdom is to use a slow shutter speed. The normal recommendation is to use a shutter speed that's twice the frame rate, for example 1/60th of a second if you're shooting at 30fps. The slow shutter speed will blur the individual frames so that the jump between each one is less obvious. But of course it means that details will be lost in the blurring.
Using a slower shutter speed can create the opposite of the "too little light" problem mentioned above for high frame rates - too
much light, especially if you're shooting outdoors on a bright day. You may need to use a neutral density filter to counteract that.
Another way to avoid the problem is to slow the speed of your pans so that there's less frame-to-frame movement.
I'd suggest you try experimenting with different shutter speeds, frame rates and panning speeds to see what does and doesn't work for your sensibilities.
