The previous review of loop quantum gravity was discussed here. Some of my objections to loop quantum gravity are listed here.
A new brief review of loop quantum gravity by Nicolai and Peeters appeared yesterday. They show all the nice things that many of us have been attracted by for several weeks (and some slower people are attracted by for several decades), especially the discrete spectrum of areas. The key point they emphasize is that the main problem of quantum gravity is the infinite number of coefficients of higher-derivative terms that are undetermined, making the theory completely unpredictive. They show that this infinite unpredictivity is, in the context of loop quantum gravity and spin foams, just translated into the infinite number of unknown parameters of the Hamiltonian or the spin foam rules.
This implies that loop quantum gravity and its variations make zero (0) progress in solving any problems of quantum gravity.
Nicolai and Peeters also argue that there is an important difference between lattice gauge theories and latticized general relativity. In the first case, one can independently take the continuum limit and the classical limit (lattice QCD). In the latter case, it is not possible, despite the (wrong) assumption of all the people who promote loop quantum gravity. Nicolai and Peeters use the fact that no physical semi-classical state has been found in loop quantum gravity which shows that the assumption is probably wrong.
I think that there is a more straightforward and reliable way to argue that this assumption of loop quantum gravity about the independent limits is patently false. The classical limit and the continuum limit in quantum gravity is the same thing simply because the "dynamical lattice spacing" is proportional to the square root of Planck's constant (recall the formula for the Planck length). Taking the Planck's constant to zero is therefore equivalent to taking the lattice spacing to zero. QED.
In other words, diffeomorphisms which must be a symmetry of quantum gravity allow us to convert a large coordinate distance into a small coordinate distance with a smaller value of Planck's constant, and therefore, these two limits cannot be considered separately (and the continuum limit cannot be taken as a separate step after the quantization). This is of course nothing more than the 487th argument that kills loop quantum gravity.
The 488th argument that they repeat is ultralocality - the inability to obtain the usual concepts of continuity of space from loop quantum gravity which is equivalent to the non-separability of the kinematical Hilbert space.