Spend BTCs from a paper wallet
The Blockchain.info Android Wallet app is open-source and has been heavily peer-reviewed by the community. Your private key is stored on the device once scanned, but it is encrypted with a password so even if you lose your phone they won't be able to access the key.

As for the using safe ROMs, Android is a very secure sandboxed virtual machine that has been rarely compromised. The encryption of your keys is based on powerful and heavily tested Java libraries which run on an open-source platform called Dalvik, which is based on the Java Virtual Machine (JVM).

In other words, you really couldn't ask for a more secure environment.