The quantum state of the Universe As far as I know, the two popular attempts to quantize gravity (string theory and loop quantum gravity) rely on unmodified quantum mechanics. Since they aim to become ToEs, this also mean that the whole Universe is described by its quantum state. It has to be pure since the Universe is an isolated system. Therefore the problem of measurement arises and etc.
My question is: is there anything new on this subject that I missed? Maybe the problem of measurement doesn't arise in string theory?
 A: It is not enough to be popular or enough to quantize gravity. A TOE has to be able to include special relativity ( Lorenz invariance) and to embed the whole standard model of particle physics. At the moment only string theories are able, have the group structures , to do this, but the specific string model is still a matter of research.

this also mean that the whole Universe is described by its quantum state. 

Why should it be in one quantum state?

It has to be pure since the Universe is an isolated system.

Why?  It is a non sequitur. What postulate states that an isolated system has to be quantum mechanically a pure state? Have a look at the density matrix formulation of quantum mechanics.

A density matrix is a matrix that describes a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in a pure state. The density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical mechanics.

What problem with measurement?  In any case if at creation the universe is in  a pure state of a "totalum" and "antitotalum " or some such hypothesis, our observations show that very soon it ends up at the inflation age with zillions of inflatons running around homogenizing the primordial soup. No pure state there.
