I see this often in legal arguments, especially (but not only) in student work -- the writer says something like "This option would arguably violate the right to jury trial," and feels that this sufficiently distances him from the assertion that he doesn't actually need to defend it.
This sort of usage is, and should be, quite unpersuasive. If you want to argue that the option would violate the right to jury trial, argue it. But if you don't think you have enough of an argument to support the position, then don't just assert that the position is "arguably" true.
Of course, sometimes a substantial possibility of some legal outcome might be enough to counsel against risking that outcome: For instance, a prosecutor might shy away from a (relatively low-benefit) litigation tactic simply because that tactic could cause the eventual conviction to be reversed, even if that result isn't certain or even highly likely. But there too "arguably" isn't enough -- you have to argue why there is such a material risk, and why this risk is reason to reject the option.
So the word "arguably" always puts on me guard that there might be an assertion being made without any supporting argument. And most of the time, that's precisely what's going on.