An end user with either too much permission or too much time  on their hands?
Perhaps they are trying to personalize the page  and don't realize that they are
effecting the Shared view?

The gig's up. It was me. Sorry. I won't close  random web  parts anymore

It happens to me too. It usually has to do with when I try to
inject VBScript into a CEWP. When I try to save the page  something in my
poor syntax makes the whole page stop functioning, and then when I
refresh the page every thing is either gone or has moved!

Yes, I've seen this kind of behavior a couple of times as well when I
include java or vbscript into a CEWP. It was more prevalent for me in
2003 than MOSS. For example, many people asked for a weather feed on
their home page, and sometimes I found that the script used to display
the external weather was just incompatible enough to cause other things
to break on the page  (buttons stopped functioning) or sometimes caused
the web  part to close. I never discovered the specifics of what in the
script was causing the problem, but since the problem was consistent and
replicable, this was easy to check in my case by removing the web part
and observing the effect. In your case, since the problem happens
randomly and not that often it would be harder to verify.