If you had quoted more of my comment you would have included my point that yes, secret arrests occur, but they are fortunately extremely uncommon. A lot of the outrage (such as it is, which sadly isn't enough) over FISA is its secret nature, and what has resulted from it.
There are many many problems with the system at large, don't get me wrong. Plea bargains seem like fundamentally abusive, and are illegal in most countries. "Civil forfeiture" is a top to bottom abuse. One could easily go on, and go ahead: feel free to work on these issues.
My point is simply that the origin of public arrest is a good one, it does seem to mostly work properly, and that it's the abuses that should be addressed, not the public nature. If we had magical cops who only arrested guilty people it wouldn't be needed. Since they don't exist, this is the best check we have,
(By the way: answering an AC's response to my comment: yes there is a qualitative difference between wgetting the records in bulk than having to go into the basement and copy them down one by one. I don't think that is a bad thing though -- life was much worse when abuses could be hidden because finding out was hard, or because access to information was essentially restricted to a secret elite).