k = 3, but the number of original clusters is much higher.

With more iterations k-means would have found more of the original clusters.

If k were set equal to the number of original clusters, the k-means algorithm would be likely to identify all of the original clusters, given enough iterations.

With k = 3, such as in the image above, k-means will always divide the data up into exactly 3 clusters.

Clusters are highly overlapping

Clusters are complex shapes

Cluster assignment is highly sensitive to random cluster center initialization.

Run k-means with many different values of k and see which one converges the fastest.

Run k-means with different values for epsilon (convergence criterion) and see where you get a stable solution after the fewest iterations.

Look at the data and try to estimate how many clusters there are.

Try a different clustering algorithm other than k-means.