Possibility of a DDoS attack
Each full node maintains a score for the peers it has connected to called banscore. Any 'mischief' on the part of the peer result in an increase of the banscore. When banscore reaches 100, the peer is in most cases disconnected.

When a node receives a transaction from the peer, it will verify the transaction and signature check forms a part of this verification process. If a malformed transactions gets continuously sent from a peer, the node will simply disconnect itself.