What are some of the flaws in the theory of evolution?

TL;DR:

Evolution is a theory based on observable science, but it is not without questions or weaknesses.

The theory of evolution, in its strictest biological sense, claims that all life on earth has developed over millions – or even billions – of years, beginning with a very simple, single-celled organism. Scripture explains that God created a wide variety of animals distinctly over the course of six, 24-hour days. Paul agrees with this in his letter to the Corinthians (1 Corinthians 15:39). Some views of evolution are compatible with the Bible’s accounts; other versions of are entirely irreconcilable with Scripture.

from the old testament

God created distinct and unique creatures (Genesis 1:20-25).
God created birds, fish, land animals and mankind according to His deliberate and purposeful design (Genesis 1-2).
God’s understanding of how He created is infinite compared to our limited perspective (Job 38-39).

from the new testament

Paul argues that the uniqueness and variety of life is God’s handiwork (1 Corinthians 15:39).

implications for today

Despite accusations against others, the evolutionist ultimately has what any other believer has: evidence, an interpretation in that evidence, and some level of “faith” in both. Christians do not believe blindly, but are called to rely on evidence, with “faith” being trust in such things (Acts 17:11; 1 John 4:1). The evolutionist might criticize the Bible for difficult passages, or apparent contradictions. Yet the theory where they anchor “faith” also presents challenges. Usually, the evolutionist will say "we just don't know yet" in the hope that new evidence will be discovered to show how contradictory forces can exist in harmony. Ironically, the ardent evolutionist's unwillingness to accept that there any weaknesses, at all, reflects blind faith—exactly the criticism unfairly used against religious views.

understand

The theory of evolution posits that all life on Earth developed over millions or billions of years from a single-celled organism.
Evidence that animal bodies have changed over time would not itself prove why the changes occurred. Nor would it disprove the influence of a Creator.
The Bible states that God created all life, making Him the reason and source for all diversity.
Evolution is a widely-accepted idea for a reason; but it is not without its own conundrums and unanswered questions.

reflect

When comparing various theories of evolution to God’s Word, how can you respect the objective aspects of science without compromising the Bible? How can you look at various theories about creation as recorded in God’s Word without dismissing genuine, real-world facts and observations?
How do you reconcile apparent contradictions between scientific evidence and scriptural accounts of creation? How can you see the difference between contradictions to certain interpretations, versus contradictions to the Bible, itself?
What role does faith play in the acceptance of scientific theories, biblical teachings, and how they agree, disagree, or overlap?

engage

Basic evolutionary theory assumes all life evolved from a single cell, gradually, over many millions of years. This is generally called "gradualism." Yet later discoveries showed some organisms suddenly "appearing" in fossil records, and / or existing for long periods of time without changing. To reconcile these, some evolutionists postulated that evolution occurred in short, intense bursts, rather than at an even pace. This was called "punctuated equilibrium."
Punctuated equilibrium is challenged by the rarity of positive (beneficial) mutations. It may require multiple organisms to experience identical genetic mutations at the same time. Delicate ecosystems would have to adapt very quickly to accommodate new creatures.
Microevolution (the proven tendency of animals to adapt to their environments) is very different than macroevolution (the unproven tendency of animals to morph into new animals over time). Some microevolution is drastic—it is amazing that a Rat Terrier and a Great Dane are the same species. But there is no visible evidence, today or in the fossil record, to suggest that a Great Dane can (and will) become a horse if given enough time.