I agree with one of the comments that one could write a book on this (I have an idea!) because this could get broad, but consider that these data mining tools (and I build them!) make some major assumptions. For instance, consider search history. One could easily build a program or a tool that would do "random" searches on topics where a person lacks interest. I've done this with Google where a program will search for dogs, dog food or dog treats and months later, I suddenly see these advertisements appearing everywhere.
if we conduct any transactions online these can all be collated to
build a good picture of what we do, buy, read etc
When it comes to finances, it's similar; I have to make an assumption that the data I receive are an accurate indicator of who you are. Suppose you make 1/3 or more of your purchases completely away from your interest, for instance, you're truly a Libertarian, but you decide to subscribe to a Socialist magazine. How accurate are my data then? Also, you may change in ten years, so how accurate will my data be then, unless I account for it (and how effective then is it to have all the historic data)?
Of course, we could all argue, who in the world would do that? If you've ever read Soros' The New Paradigm For Financial Markets he mentions his family went through WWII without the trouble many Jews had because, as I interpret it, his family was careful with the information they provided to others. Privacy, historically, is priceless, even if a few generations mistakenly think it's not.
As a note, this answer only addresses the above concern with money.