In some states, they might consider a weapon to be concealed if it can't be readily identified as a weapon. It doesn't necessarily matter if part of the weapon is visible; if you can't identify it as a weapon then it's concealed.
For instance, with a knife clipped into your pocket, they could argue that it's concealed because the average Joe can't immediately identify it as being a knife. He might think that it's just a pager, cell phone, flashlight or pen clipped into your pocket. It's obvious that something is clipped there, but it's not clear what it is.
I personally think that's a pretty silly argument, but it's something to watch out for.
Like Medusa said, there's really never a clear answer for this kind of question. It depends on so many things: the officer; the DA and AG in your state, county or city; case law and statues; how you conduct yourself and how your lawyer conducts the case; etc.. It's very frustrating trying to get some idea of whether or not this kind of thing is legal.