It came out in the finnish camera forum (http://www.digicamera.net/keskus/view...) that Lightroom will crash if 1x1 photos are imported to Lightroom 4.1. One person was able to reproduce the problem by importing 1x1 jpeg files created using MS Paint, and other person was able to reproduce the problem in Vista 32 bit.
I do not have samples, because people in the forum has some problems to upload such photos and I do not have access to Windows. Mac seems to be immune to this problems, at least I couldn't reproduce this in my Mac using 1x1 jpgs created with Photoshop. But anyway, there seems to be a way to generate such photos (Paint in WIndows).
I guess it's quite uncommon to have 1x1 files, but problem in this case was that the person tried LR first time and did an initial import using all of his files. First crashes appeared just random crashes and it took a while to figure out what was causing the problem. So I think it could be better to fix the problem than let some other people who are starting to use LR struggle with the same problem again.