I need to travel to the Philippines for a week, my green card date of birth is off by one date. But my passport is correct. Do you think I can go there and come back to the US without any problems?
While it might cause a delay in Immigration as you return, if you have sufficient time before departure, you might want to go ahead and correct your records.
USCIS has an online tool to expedite the process and, in particular, when it contains such a typographic error.
Even if your card is not re-issued in time, the system would reflect that a correction is in process.