The MAX1555 (and MAX1811 for that part) charge the batteries with up to 4.2 volts, a voltage which is distributed to all components of the player. According to the VS1001 and VS1011 datasheet, the absolute maximum voltage that may be supplied to it is 3.6 volt.
Is it really still ok to feed it with 4.2 volts, or am I missing something? I have a feeling I do... Especially as this design seems to be used for most DIY mp3 players out there.