What client-side checks does blockchain's android client do?
The quote in the documentation is a remnant from the http://code.google.com/p/bitcoin-wallet/ which the app was forked from. 

At present it does not do any blockchain validation. I would like to have it so instead of downloading the full transactions from blockchain.info the client asks for the block hashes that contain transactions of interest. It can then download the full blocks from the p2p network and only the headers for other blocks to verify the proof of work. However this is not currently implemented.