Any Problem in Letting iPhone 4 Battery Drop to 0?

Solution 1:

Not really. You won't suffer any data loss because the iPhone keeps everything on non-volatile flash memory. A complete discharge isn't great for the battery, but as long as it's not a regular habit your phone will be OK.

Solution 2:

It should not be problem, but avoid leaving the battery in an uncharged state as this can cause it damage. The phone turns off before the battery is completely discharged anyway to guard against this just don't leave it for days like that.

Apple recommend having a complete battery cycle (go from fully charged to depleted and back to charged again) once a month anyway.