Why are broadcast checkpoints considered bad? warren, a LiteCoin dev, said of Peercoin:

Good Luck Removing PPC's Centralized Checkpoints
Regarding PPC... these amount to empty obfuscating defensive excuses.  Sure he wants to remove the broadcast checkpoints.  Novacoin's Balthasar made similar promises because he too knows that it is indefensible.  Unfortunately for PPC, in the age of ASIC's it will be impossible to keep a sha256d network stable without it, so I would be highly surprised if it is actually removed.

Why are broadcast checkpoints so indefensible? It would seem to make sense to have a protocol-level mechanism whereby the nodes agree not to go back past a certain number of blocks (say 10 or 20 blocks). What about the mechanism is flawed? It sounds like it's able to keep a network stable without requiring as much hashing power.
Centralized checkpoints is a mechanism whereby nodes trust a certain hardcoded key to make new checkpoints. This means that in case of a fork, the key owner can make the network choose any branch he wants, even the one which is shorter. If this key is compromised, an attacker can use it to mount an equivalent to 51% attack with any hash rate. This, together with that the developer should constantly do something (produce checkpoints) to keep the network secure, goes totally against the idea of decentralization. Without decentralization, a cryptocurrency has little advantage over traditional banking system.