It is a bad thing because it leads an already staggering expentiture level (over $ 1.7 trillion worldwide in 2012 alone, $ 711 billion by the US) to rise even more steeply.
Apart from the financial waste, an arms race - or a case where one country starts outspending its neighbours or tries to outgun them by developing atomic bombs - can easily fuel political tensions as presently shown in the case of China, Iran and Korea.