Struggles with a high number of dimensions, need to use PCA or spectral clustering to help fix issue.
Choosing K value manually/based off of your domain knowledge of the problem. Need to use elbow method to assess best K value.
Sensitive to outliers.
Sensitive to initialization.
Now imagine the points are more widely spread out, we still have the same centroids even though it's not the best option. If the initial centroids are not chosen properly this can cause problems later.