Sampling effects like this can be really pernicious for network data (and I imagine similarly for other dependent data). It can be difficult to tell if a network is scale-free from observing a subnetwork [1] or impossible to learn an ERGM (basically, a maximum entropy distribution with graph properties as its statistics) from a subnetwork [2].
A popular-media take on a subtle problem in sampling. I found the graph quite illustrative.
http://www.theatlantic.com/business/archive/2012/05/when-correlation-is-not-causation-but-something-much-more-screwy/256918/