Evolution is a fact. But can all facets of life be exlained with the neo-Darwinian theory of evolution alone?
I don't think so, and I have elaborated the reasons for this appraisal in a detailed book about enigmas of evolution (Nahm 2007).

1. The Origin of Life
The first and foremost enigma of evolution concerns the origin of life. Although one might get a different impression from following discussions in the public media, it needs to be stressed that until today, scientists have no clue about how first cells and molecules like the DNA came into existence.

On close examination, it becomes obvious that at present, all we have are highly speculative and problematic hypotheses that are built on questionable experiments with largely disappointing results.
Even fashionable concepts of self-organisation and computer models like 'hypercycles' couldn't change this situation. Consequently, leading experts in the field of probiotic chemistry have conceded a lack of progress and success in their research discipline.

In my book, I have described 24 profound (bio-)chemical difficulties that need to be overcome in theory and in practice before it can be assumed that we know how life emerged on our planet.

Still, despite all obstacles, life appeared on earth. According to the standard theory of evolution, the first cells developed into increasingly complex
organisms by random mutations in their genes, and by subsequent selection of the best adapted individuals. Although this theory seems appealing on a superficial level, numerous serious problems emerge as soon as we ask deeper questions about some of its most problematic implications.
Understanding these problems in adequate depth, however, requires diving into intricate biological details, and there is no space for this on the present website. I will only add a few general comments on mutation and selection in the following.

2. Mutation
Regarding the concept of random mutations as the substrate for developing higher complexity, it should be noted that past scientists have explored the creative potential of mutations in huge and detailled studies. Literally millions of random mutations were generated in numerous animal and plant species, e.g. by exposing them to X-rays. Yet, the very few mutations that could be interpreted positively under certain circumstances always concerned the loss of previously existing traits, or the modification of an already existing metabolism pathway. Stable mutations that would have resulted in the generation of a new and useful structure were completely lacking. Despite enormous initial expectations, this line of mutation research was entirely abandoned by disappointed scientists already decades ago.

3. Selection
Just like mutations, natural selection among living organisms does occur in nature. But does it explain evolution? Biologists disagree with regard to answers to this question, and they advanced several different hypotheses revolving around selection processes. On close examination, however, all of them lack a concrete and continuously available point of action that would explain the development of innumerable organismic characteristics, especially of many macroscopic characteristics.

Just take the peacock. Already Charles Darwin tried to explain the development of its train and ocelli via sexual selection - i.e., for generations, the peahen would have
always selected the most magnificent males for mating. This explanation was doubted ever since, and indeed, recent studies confirmed that it doesn't seem to apply in this case.

But, more importantly, the peacock is a prime example that illustrates how the result of supposed sexual selection can completely override an ideal body shape that would be useful in the purported continuous struggle for survival. If the peacock can survive with a severe handicap such as its train, then natural selection can only be regarded as a very tolerant judge of life and death, what is as at odds with the traditional neo-Darwinian view.
And the peacock is only one example out of many in which the macroscopic appearance of an organism cannot be explained solely by merciless selection processes that eliminate all suboptimally adapted individuals. 

For example, look at the amazing wealth of shapes and colours of the fruiting bodies of fungi. Clearly, the macroscopic appearance
of a given mushroom species has no bearing for its commonness or 'fitness.' Without exception, specifications on the physiological level determine whether a fungus species is common or rare.
This appraisal is also valid for many (but not all) plant and animal species.

But, as mentioned, these are only a few general comments about mutation and selection. There are many more problematic aspects regarding these two pillars of neo-Darwinian evolution theory, but they require more subtle considerations. In my book, I have elaborated them in detail.

A living being appearing in a hostile environment
(Schreckhorn; Photo: M. Nahm)

Abnormal blossom development in the late
spider-orchid (Photo: M. Nahm)

Indian peacock displaying (Photo: M. Nahm)

Yellow stagshorn (Calocera viscosa), a very
common mushroom species (Photo: M. Nahm)

The "March mushroom" (Hygrophorus marzuolus).
Typically, it grows in March and it is considered
very rare in Central Europe (Photo: O. Nahm).