A longstanding problem with SPV at receiving is the lack of full validation: You'll have trust a collection of other nodes to not all defraud you. This is typically "solved" by randomly choosing your node connections (still kinda vulnerable if the attacker is very resourceful) or trusting a third-party node (model used by Mycelium).

But if you already run a node, get your SPV wallet to "trust" your own node, and you have your full node's security in your hands. Yes, there is a benefit to running your own node, other than altruism!

To do that in Schildbach's Wallet (Android, "Bitcoin Wallet"): Settings -> Settings -> Trusted Peer. Specify the port if it's not 8333.

That's the only SPV wallet I use, others can chime in about the other wallets and how to set them up.