Just back from a four week trip thru Vietnam and the bordering countries. It seem that In Vietnam , you really need to be on your guard as it is so crowded and within the market area esp. Saigon , they do grab hold of you and pull you into their stores. I spent 7 days in Saigon as part of a large work group and numerous drive by robberies occurred within our group even necklaces were snatched by motor scooters thieves. It is happening so be careful. Also , no matter what the regulars say on this forum, be especially careful of the cyclos . Do not take these at night, you will not know where you will end up or if you are lucky they will only try and extort money from you.
If you stay in a decent hotel, use your room safe as they are common in most hotels throughout Vietnam or use the hotel safe. I prefered the room safe. You will find that the hotel will hang onto your passport and this was no drama.
As far as money goes, $100 goes a long way on the streets of Vietnam so just carry what you need and use the ATM if you require more. No dramas finding an ATM. You can buy a money pouch from bag shops in Aus that you wear under your clothing for your cash if you wish. I used one when i was on the move for my passport , cash and credit cards. After a while you forget you are wearing it and it gives you some peace of mind.
Hope this Helps