Under what conditions does 60hz video produce visual artifacts? There are some important thresholds of frame rate in video playback that effect whether or not animation appears fluid. This wikipedia page about Visible Frame Rate suggests that a framerate of 60 hertz doesn't quite provide enough information fast enough to be seen as fluid in some cases:


  However, fast moving objects may require higher frame rates to avoid judder (non-smooth, linear motion) artifacts


When exactly does a higher framerate become necessary? What studies have shown what kinds of motion cause this "judder"?
The Wikipedia article no longer makes reference to the phenomenon that you quote (to my inspection), so I'm not entirely sure if that assertion was edited out as an inaccuracy on someone's part.  I did find some information on visual perception and high frequency flicker that might point to some of the significance of the 60 Hz refresh rate of a monitor.

At first I thought the effect you were describing might have something to do with critical flicker fusion frequency.  This is the rate under which the blinking of a light is no longer perceived as continuous.  For humans this varies from about 37 to 46 Hz (when measured as frequency of stimulus offset and remeasured over the course of the year) and from 43 down to 36 Hz (when measured as a frequency of stimulus onset and remeasured over the course of the year), so if a light blinks at a rate higher than that, it will look like it is continuously on to the average human.**  However, since 60Hz is just shy of being a harmonic for the human critical flicker fusion, this seems like there wouldn't be some type of aliasing effect, as there is no 30 Hz component.

What I did find seems to be a plausible reason for some sort of visual entrainment with a 60Hz stimulus, but even the authors of the study (Williams et al 2004) rationalized 


  [If this were the case] perception should be compromised noticeably when looking at television or computer displays that have 60 Hz (or 50 Hz) frame refresh rates. However, every day more than a billion people watch TV with no obvious distortion in their perception of the color, form, and motion of pictures on the video screen. Thus phase locking in the middle of the gamma [brain waves] band [40 - 100 Hz] that is irrelevant to the visual scene does not disrupt scene organization or corrupts it so subtly that people do not notice. 


That being said, that group performed a very careful study on both humans and non-human primates and found that between 32% and 82% (the percentage increased based on increasing contrast of the stimulus) of "cells" (single-units) studied in primate V1 over all animals were entrained to a 60 Hz refresh rate of the CRT screen.  The human Visual Evoked Potentials (using a non-invasive EEG) were all found to be significantly entrained to the 60Hz CRT refresh rate, and were also seen to increase with stimulus contrast.  For higher refresh rates of 72 Hz and 100 Hz, the degree of entrainment decreased significantly.  So, in both sets of subjects, the 60 Hz flicker induced significant 60 Hz activity in the brain.  Activity in the gamma band is normally associated with binding non-local cell assemblies for the purpose of cortical synchronization.  

In contrast, though, Bauer et al (2012) found that flickering two "flanker" targets pulsing in phase at 60 Hz while surrounding a central primary target with low contrast did not enhance the ability to see the central target compared to a scenario with two flanker targets firing at 60 Hz out of phase with each other.  Building on other work that has been done, they hypothesized that synchrony of neurons in the gamma band (40-100 Hz) would directly help in "mediating contextual interactions among local stimulus attributes".  For this study, 60 Hz was chosen as the "typical frequency for human visual cortex gamma oscillations"  The thought was that the pulsing 60 Hz stimuli would entrain the gamma band oscillations in visual cortex to prime the system for stimulus discrimination.  A setup with "in phase" flicker of the flankers with the central target was not found to help in the discrimination of orientation of the primary stimulus either.

So, overall, the 60 Hz seems most likely to have gamma band entrainment effects, but as a caveat, these effects don't seem to significantly hamper our ability to perceive motion on the screen.


**As an aside, I also found a study about the flicker fusion frequency in chickens (which, for some reason, have become a testbed for visual perception tasks).  According to an earlier study cited in Railton et al (2010), hens have a critical flicker fusion from 69 Hz to 105 Hz, which is in the typical refresh rate range for CRTs, so the authors of the study found that using thin-film transistor screens was more effective in stimulus discrimination tasks.  So, presumably the 60 Hz CRTs would cause a choppy motion from the perspective of the chicken, but I'm not sure this would account for any judder either. 


References


Bauer, M., Akam, T., Joseph, S., Freeman, E., Driver, J. (2012) Does visual flicker phase at gamma frequency modulate neural signal propagation and stimulus selection?  Journal of Vision 12(4):1-10. [DOI]  [Free PDF]
Luczak, A., Sobolewski, A. (2005)  Longitudinal changes in critical flicker fusion frequency: an indicator of human workload.  Ergonomics 48(15):1770-1792.  [DOI] 
Railton, R.C.R., Foster, T.M., Temple, W. (2010).  Transfer of stimulus control from a TFT to CRT screen.  Behavioural Processes 85:111-115. [DOI]
Williams, P.E., Mechler, F., Gordon, J., Shapley, R., Hawken, M.J. (2004).  Entrainment to video displays in primary visual cortex of macaque and humans.  Journal of Neuroscience 24(38):8278-8288.  [DOI]   [Free PDF]