Cannot reproduce this bug with current trunk, please try with a build from http://builder.blender.org/download
Also always please specify minimal steps to redo the issue (from your "no bevel" file, I simply hit ctrl-B, and wheel to increase number of edges, everything looks good to me...).
Windows 7 Professional 64-bit
ASUS nVidia GeForce GTX 760 2GB GDDR5 DirectCU Mini
Blender 2.70 hash - 8f1a6e2
I can confirm this behavior on my system:
lopataasdf has posted the images of how the bevel function is going wrong.
In this case, when more than one bevel segment is used, the profile setting is not being taken into account on every edge line passing through the profiled area.
This same problem can also be seen in the Blender 2.69 bevel function. There is no profile setting there, but the curve of the edges passing through the beveled area is also not always correct.
anyway i reccomend you to use the bevel as a modifier+weight, so you can control, which part/vertex or edge should be beveled and how much. i never use the standard bevel option and actually its unnecessary.
Howardt, I can still reproduce the bug mentioned in the first post in today's build. That means edge loops which are close to each other still don't follow curvature and go straight. Just try a multisegment bevel on an edge loop.
The problem here is that you have edges totally in a plane (both the two edges to be beveled, and the two cross-edges on either side), and you want the multisegment bevel to be curved. I know that in this case, where they are running beside other edges that curve (because they aren't all in the same plane), it looks like a mistake. But there are other cases where making them curve can look wrong. So not clear what to do here.
Here's a situation where making the cross-edges curved is not obviously the right thing to do. On the left is the edge to be beveled. In the middle is the current behavior. On the right is the result of an exploratory hack to recognize "being flat in a plane" as a special case and making them curve. (The outside edges don't curve because that's even more of a special case in the code that would have to be changed separately. Is the curved image always better and should I continue down this path? On issue could be that it is fragiley adapted to a special case, and making small changes in geometry could cause big flips in behavior. This could be the start of a long path of special cases to get this right...
The behaviour I would like is in the following image. Which means curved inside and outside edges included. The current behaviour really doesn't behave like a multisegment bevel. I could get the same with 1 segment bevel and then add loopcuts. So I think it's definitely worth continuing this path.
I have a branch that partially fixes this, but it is not working correctly everywhere, yet, and is too big a change to put in the close to the next release. I continue to work in the branch and hopefully will commit the change after the release.