Yes, the type of data you are asking about does exist, but it isn't available for curious passengers to critique.
Most modern airlines have within their safety programs a means to record and analyze data and flag events that exceed certain parameters and are on the margins of safe, or "normal" operations. The event can then be reviewed in greater detail by experienced flight crews and safety experts with the intent of determining whether or not any procedures were violated. This is all done in the interest of improving safety, not for explaining to someone why a certain landing felt "wobbly".
There is some additional information in the article here: Flight Safety
Something would have to rise to the level of a reportable accident for the NTSB to get involved, and for the results of the investigation to be made available to the public.