Hey Emiel,
Is your timeline set to progressive?
Or are you rendering it out as a progressive file?
Keep in mind that in the olden days of shooting 24 fps on film, the DOP had to be careful with pans. Same goes with the basics of working in progressive on digital, in a speed that matches what the frame-rate can handle before you start getting problems in motion effects.
There is a number of effects that you can add to make better (smother), such motion-compensated frame interpolation, but is all based on trial and error.
Alternatively slow the shot down, or make it run for longer.
One quick and dirty trick that might work, is to export out the effect shot interlaced to a high-quality video-file, and then re-import it into the progressive time-line.
But one thing that you can be sure of, is that if your relatively small monitor picks it up, there is every chance that a large cinema screen will amplify the issue.