Currently, there are about 5-6 pools who mine around 75% of the whole Bitcoins. If you target those pools with DDoS attacks, you can make them unstable, failing, etc. The result would be 4 times slower Bitcoin network.
Sure, new pools may show up. It will take some time, though. And they can be targeted, too.
Actually, I think that the above is already being performed by SOMEONE.
So how does that affect the safety or security of BTC?
During the time that 75% of the network hashing power isn't processing, a malicious group only needs to overcome the remaining hashing power to double-spend.