What is wrong with Ernest Haekel's idea of evolutionary recapitulation during development is that it is a gross oversimplification of both developmental and evolutionary process -- it does violence to the subtlety of evolutionary events and the plasticity of development.

As stated by Haekel, recapitulation requires that each species passes through all of the adult stages of its ancestors. This is clearly incorrect.

Natural selection can act at every stage of an organism's life - from early development through the reproductive adult.

While it was originally thought that the early stages of embryonic development were particularly sensitive and could not be easily changed -- it is now clear that early developmental stages are as plastic as other stages -- the organism is adapted to all stages of its life history. In fact, one can even see different stages of an organism as having conflicts with one another.

For example, senility upon aging is due in part to selection for traits, while disadvantageous in the old, are advantageous in the young.

All vertebrates share a common body plan -- and pass through a more or less similar phyllotypic stage.

But they can differ rather dramatically in earlier stages.

The relative timing of different events can be altered, with dramatic effect on organismic morphology.

For example, the oft cited statement that all early vertebrate embryos have gills (as does an adult fish or larval amphibians) is not true. The structures that form the gills, the pharyngeal pouches, in fish form a number of completely distinct set of structures in mammals (see this link as well). Morphologically similar embryonic structures have, under the influence of selective pressures, given rise to distinct adult tissues.

In terms of human evolution, the idea of recapitulation has often been used to paint "primitive" peoples into a position on a lower rung of the ladder of cultural development.

In this view, such "primitives" will have to pass through the same steps of cultural/psychological evolution as has occurred in western Europe to become as advanced as Europeans.

This is a version of obsolete idea of the "Great Chain of Being" and ignores the fact that all cultures are shaped by historic accident and environmental constrain, rather than an almost supernatural destiny.