The quick method to circumvent an iPhone's passcode-protected lock screen: tap the "Emergency call button," then four pound signs, [then dial] and immediately hit the Lock button. That simple procedure gives a snoop full access to the Phone app on the iPhone, which contains the address book, voicemail and call history.
You can't run other apps, but you can examine the entire address book, and make phone calls to arbitrary numbers. (Clicking on a URL in the address book won't launch Safari either.)
Weirdly, the phone will stay powered up until you initiate a call.