Asked the receptionist at my guesthouse in Rangoon if it was OK to fold my crisp USD notes so I could keep them in my wallet. She said no and made me a container out of paper to keep the notes in (cardboard seems like the best solution). That was a stack of $5-$20 notes. I had no problems paying some entry fees with well used $1 bills though. For future record: they had no tears (well, maybe a microscopic one on one of them) or stains, but had been folded and one was even a bit faded. Hope someone will report back if they try to change or pay with larger notes in less-than-perfect condition.

There are different rates for different denominations of USD in Burma, but even $1 notes can be exchanged if you are willing to accept a slightly lower rate. At the time of writing, USD, EUR and SGD can be exchanged by official money changers, e.g. at Rangoon Airport.

Most things can also be paid in kyat nowadays. Some people even said they paid their accomodation in kyat. Several ATMs (dispensing kyat) that accept foreign cards have sprung up in Rangoon. Haven't tested any myself, but I have heard about people using them successfully when there is power. Better bring some USD in cash as backup for the time being.