Analysis of dataset is difficult when there is too many variance lays over it, noise or deviation is to big and wide area of data spread. Most of its came from wide are of data spread, from statistical view range on distribute frequenti are to close but the data set spread rarely on that range
In my profession, I have come across some BIG MESSY DATA, though could not be considered MESSY BIG DATA!! There were times when I had to find a way to replace missing values. In most of the cases I chose to replace the missing values with the sample mean or median. In other cases, I made use of the dummy variable adjustment or I replaced the missing values with the predicted score from a regression equation.
But I must emphasize that I personally try to sort out the problem of cleanliness of data from the initial stage of collection itself. What I found in practice is that many researchers first collect the data and only afterwards they get worried about the cleanliness of data when they encounter some problem during the analysis of data; sometimes, this realization comes too late, and they have to re-start the whole research!
Much problems mentioned above are technical issues and might be solved by algorithms or data structures (size, dimensions, variance, etc.).
I agree with Tatiana, one of the factors that make it difficult is the quality of your data and preprocessing, cleaning, selection, transformation are very important steps.
But the main factor, in my opinion, is the expert knowledge. When you want to solve a problem on your own and apply your brand new algorithm to a dataset because you want to publish a paper, that is not a big deal (you want response times, or memory consumption and that's fine). But when it comes to a useful data analytics, with results that will have impact in a specific domain... then you'd better have an expert who will understand your analysis or... be the domain's expert yourself!
Expert knowledge is a key. It takes time to build. Or it takes time for an expert to understand the techniques and results of data analytics. But it's worth the time spent!