In 2002 my wife and I flew Thai from BK to Saigon and Thai from Hanoi back to BK 3 weeks later.
Vietnam Airlines should probably be OK as I believe they don't fly those Aerflop Commie Russian lead ballons anymore.
There is one alternative that you may consider. Air Asia is now flying Hanoi-BKK. Check the price on Vietnam & Thai Air; HCMC-BKK and then Hanoi-BKK on Air Asia. It maybe worth ending your VN segment in Hanoi and flying to BKK from there. Worth checking at least.
Airlines for Bangkok from Veitnam are 1)www.thaiair.com 2)www.veitnamairlines.com 3)www.airfrance.com
But while you are on your great adventure why not do the Mekong River boat trip and bus or shared taxi trip from HCMC(Saigon) to Phnom Penh,(arrange at travellers cafes in HCMC,Pham Ngu Lao area).
Stay in Phnom Penh for a few days then bus to Cambodia beachtown at Sihanoukville for a few days then a boat(5hr) upto border at Koh Kong then taxi to Thailand border town of Hat Lek and into Trat for a day.
"Then AC bus" with great roads along beautiful Thailand coast and Islands(Ko Samet) and maybe jump off and stay for 1-100 days just enjoying ones travels and the ability to do it,dont go home and say I wish!!.
I remember that road you travelled,I called it the dusty road with rotten bridges and superfast sucide bus driver,I loved it!!!!!!
Have great fun travelling and enjoy Veitnam.
al de bes
Airasia will be the cheapest way from Hanoi to Bkk. If you are ending up in Saigon though, expect to pay just over $100 US one way. Thats what i paid in June flying with Vietnam Airlines. If you do end up in Saigon get them to check Thai as the travel agents generally just give you the price of Vietnam Airlines and tell you that is the cheapest fare.
I would suggest looking at the Discovery Airpass.
I have found it to be good value for intra Asia flying.