Mean field theory gives sensible results as long as one is able to neglect fluctuations in the system under consideration.
The Ginzburg criterion tells quantitatively when mean field theory is valid.
It also gives the idea of an upper critical dimension, a dimensionality of the system above which mean field theory gives proper results, and the critical exponents predicted by mean field theory match exactly with those obtained by numerical methods.
If the dimension of the space is greater than 4, the mean-field results are good and self-consistent.
For instance, in one dimension, the mean field approximation predicts a phase transition at finite temperatures for the Ising model, whereas the exact analytic solution in one dimension has none (except for