A little complement to HDunn's answer :
Sentinel-2 is still in "ramp-up phase", and does not perform yet ortho-rectification with ground control points (GCP). A location error of only 30 or 40m without GCP is in fact excellent, but not sufficient for users. However, usually the performance is better than 20m, but there was an issue on the orbits around the 15 of August, because of a manoeuver to avoid a debris.
When the ortho-rectification with GCP is implemented, errors will be reduced to a few meters. I do not have a clear view of when ESA will start processing the data with GCP. At the Living Planet Symposium, in May 2016, ESA announced it would start end of 2016, but I do not know if it is confirmed.
There are usually no visible shifts between the strips on the earth surface, but shifts may be observed on the clouds. This may be explained by the fact that odd and even detectors (which correspond to gray and white strips in HDunn drawing) do not exactly look in the same direction, this is compensated by the ortho-rectification using a DEM, but it cannot be compendated for the clouds as their altitude is unknown. However, Sentinel-2 is not designed to watch clouds (although it does a lot !)
If my explanation is too short and complicated, there is a much deeper discussion here :