I think you have the wrong image in your head - it WAS flattened, 60 years ago. Today, you won't see any debris or something caused by world war two anymore...
I suppose there is racist assholes anywhere, not just in East Germany. I don“t think there are more in Germany nowadays, than in any other European country, leave alone in Australia, or the States. However, in all these countries they are just treated as what they really are f***ing loonatics, but in Germany we have a good reason to be more alert.
Last but not least there are people who beat other people up just because they were "just there". This happened to a friend of mine. He got kicked in his faces severel times, just because he was at the wrong place in the wrong time. This can happen to you almost everywhere on the world. But don't be terrified. I don't think it's more dangerous here then everywhere else. If you want to feel safe, don't go alone. That's what I do.
An interesting atricle concerning the topic here: http://www.dw-world.de/dw/article/0,,1991934,00.html?maca=en-aa-wm-1072-rdf
A bit OT but, back in 2000 or 2001... I skipped school and was hanging around Mannheim with my buddy on Maitag (May Day) which I had no idea what that was or that the day was Maitag... and I ended up in a group of NPD supporters. The NPD is a pro-nazi political group I believe, and what was funny is that I'm not what you would consider Caucasian, even though I do have European lineage... but I'd always be mistaken as Hispanic in the Southern US states, or Indian in the Northern states, and of all things, Turkish in Germany, lol. The NPD supporters never bothered me, I even bummed a couple of cigarettes from some dude. Being in W. Germany, the people are more friendly... but when I was in Berlin for the Hanfparade back in 2002 I ran into some fellow with a shaven head and I was trying to ask for directions to the U-Bahn, but the guy was a prick and said something like "No" I think, can't remember what exactly he said, but I noticed he was watching me when I asked a boyfriend/girlfriend couple for directions to the U-Bahn. The shaven head fellow didn't bother me, but I did notice in my peripheral vision that he was watching, I think he was thinking that I was possibly asking for money perhaps? Who knows.