I have a leaky outdoor faucet. I replaced the washer in it but it still leaks. Does anybody know what else could be the cause of this and what I can do about it?

Chances are good the seat is bad too. That new washer should be pitched out because it is now scored by the bad seat. Buy, borrow or rent a faucet valve seating tool and reseat the place where the washer makes its seal. Some faucets have replaceable seats, look inside to see if there is a medium sizied Allen wrench hole, that's a replaceable seat.