The one I'll point out is using a dead person's birth certificate to get ID and an SSN. The databases for the death index were cleaned up after 9/11 and if you try this, your attempt will be flagged and you'll likely be visited by law enforcement pretty shortly. You will not get an ID nor an SSN.
The best way to hide is to not leave any (legitimate) money/electronic trails. Practice disinformation. For example, use a credit card to buy a plane ticket to Bangkok on Saturday, then go buy a bus ticket to Mongolia with cash for Friday and similar tactics. It won't stop professionals from eventually finding you, but it will buy you (sometimes significant) time.
All this is pointless because almost certainly the US IC knows exactly where Snowden is already. It's laughable that anyone believes they're still searching for Snowden.