There are a variety of actual problems with AnCap, if only because there are actual problems with all political systems. Here's one off the top of my head. (and I didn't write this, James A. Hammerton did; the essay is really about libertarianism in general, but it applies. Anyway, it's from here: http://web.archive.org/web/20010407063531/http://www.tardis.ed.ac.uk/~james/politics/libcrit.txt )

"I will now discuss a consequence of the `freedom as absence of coercion'
position which makes it sit uneasily with libertarian ideology. If we
take this definition of freedom then the amount of freedom a person has is
the extent to which they can act without being coerced to do (or not to do)
something against their will. In a libertarian society you cannot
(legitimately) do anything with another's property if they don't want you to,
so your only _guaranteed_ freedom is determined by the amount of property you
have. This has the consequence that someone with no property has no
guaranteed freedom, and that the more property you have, the greater your
guaranteed freedom. In other words a distribution of property is a
distribution of freedom, as the libertarians _themselves_ define it.
Thus, taking this definition of freedom, and a belief in the free market
together, the libertarians are saying that the best way of promoting freedom
is to allow some people to have more of it than others, even when this leads
to some having very little or even none (as I believe is quite likely in a
free market). I don't think that this is what libertarians want, I think
they want everyone to have a sphere of equal guaranteed freedom, but a free
market does not give everyone such a sphere, and does not guarantee anyone
any freedom at all."

Also, on the subject of defense: Private defense firms could band together and establish oppressive mini-police states with little fear of reprisal. Considering that the "let's dominate those bitches and kick their fuckin' asses!" mentality is common among military personnel everywhere (this mentality is really just part of some people's innate nature, and these people are often drawn to the military), this doesn't seem too outlandish. Note that in Africa--where governments are so impotent that, for all practical purpose, they function quite a bit like anarcho-capitalist societies--military coups are rather common.