No, there aren't! Avoid big crowds and demonstrations/manifestations, just as you should do anywhere in the world.

Just to put it in perspective:

The article is discussing a certain subway/elevated interchange at a popular (or rather: very populated) square in the district of Kreuzberg.

The "Kottbusser Tor" square had always been a somewhat shady part of town since I moved to Berlin in 1992 (and before).
Those people who say that the area has somewhat deteriorated are correct when they compare it to 2005. But they probably have not been around in the 1990s when the different gangs of Kreuzberg controlled the area. Now THAT had been rough times. No more gangs, by the way.

You have pickpockets, many drug dealers, homeless people, but also tons of nice ethnic eateries, 24/7 flower and grocery shops, cheap housing estates, upscale restaurants, hipster cafes and clubs sharing the very same space.
So it would be nonsense to say that you can walk there 24/7 without paying any attention to your surroundings (and your belongings).

The oddity is not that it could become a "no go area" (which it is not - it's seriously crowded also at night) but that it's an area where "good and bad" are just an arm's length apart.

There is nothing wrong in avoiding the "Kottbusser Tor" square if it makes you feel uneasy. You don't have to worry when using the elevated or subway crossing the square, by the way.
But by proportion, the questionable area is the size of a football field in a pretty huge district.

<i>I don't mean to sound naive, but are there really areas in Berlin that we should be avoiding for terrorist reasons?</i>

That's not a naive question, but probably THE question that keeps thousands of people at the intelligence and police services busy every day.

So far, there have not been any specific warnings - aside from the general worldwide warning to be vigilant.

Locals use subways, train stations, crowded places like always and attend large festivals or street parades like always.
Last weekend, I went with some friends to the Spirit of Istanbul (food & music) festival in a major indoor venue in Berlin, together with appr. 1,000 other people. And had lots of fun (and raki).
Other people might not have enjoyed it and preferred to go elsewhere - due to the recent attacks on Istanbul and Brussels.
Depends more on each individual person's comfort zone, IMO.

I really wouldn't stress about this too much OP - the public transport system in Berlin is excellent and even if you don't have nightlife right on your doorstep, if you are next to an S-bahn or U-bahn station then you can be somewhere a bit more lively in 10 mins or so.

Link to my recent TR comparing two hotels, both in Mitte, but one more central, and one right by Berlin HBF:-

http://www.fodors.com/community/euro...he-lindens.cfm