Does it hurt the network to reuse addresses?
Reusing an address is a security issue if you have a weak random number generator, as was an issue with the Android Bitcoin Wallet. I should note this was android's fault for using a bad generator and was fixed quickly by the app developer, though some people lost coins because they had signed multiple messages (i.e. transactions) with the same address and the number generator used the same random number for more than one transaction, for more info you can see this: http://gigaom.com/2013/08/12/why-bitcoin-users-using-android-wallet-apps-need-to-upgrade/

If you'd like to know more about why using the same random number in two messages is bad, you can read about ECDSA (ecliptic curve digital signature algorithm) here: https://en.bitcoin.it/wiki/Protocol_specification#Signatures

Also if you are concerned with the people you transfer bitcoins with knowing how much money you have and when you're sending money, and possibly to whom, you should consider keeping your addresses and transactions separate. This involves choosing which inputs you use to send transactions, using a system like armory allows you to do this.