It's not easy to choose - and maybe the video's argument is cumulative, but if I had to choose just one I think I'd probably be considering the non-purposeful nature of mutations.
To get from a single-cell to modern man through a series of non-purposeful and random mutations is - I admit - an argument from incredulity, but then it often seems that the idea of God creating distinct fully formed animals kinds also seems to get dismissed out of incredulity, which means, as previously suggested, it is more a case of how one interprets the evidence.
Mutations provide the variation between individuals that make some cope a little better and some a little worse, which is reflected in the number and viability of their offspring. Over time the population will consist of variations of the offspring of those that coped the best. You should be able to see how this will result in the population changing over time.
Small changes over relatively few generations, e.g. a few hundred, are often called 'micro evolution'. Once two populations of a creature have become sufficiently different that they generally don't interbreed, or they're considered to merit being considered separately, they will be called separate species (or subspecies). This point is sometimes called 'macro evolution'.
If you're wondering how major changes came about, such as very different body plans, number of limbs, etc., the basic body plans arose fairly early in multi-cellular life, and involved mutations in the networks of genes that regulate embryo development. This is a rather complex and technical field, but the principle is that structural development is modular; limbs, body segments, etc., are produced by sets of genes and their number and position is regulated by other sets of genes.
So a mutation in a regulator gene can cause major body structure effects, e.g. achondroplasia, extra digits, even extra limbs. In highly specialised creatures these mutations will generally be a major disadvantage, but in relatively simple early life there would have been strong competition between creatures with many different body plans, eventually resulting in the fairly limited number of basic body plans we see today.
If you accept microevolution and speciation (macroevolution), What particular step(s) in the process from early single-cell life to contemporary multi-cellular life do you find problematic?
Where do you suppose God might step in, and what evidence should we expect to find of this - i.e. how could we distinguish between natural evolution and the hand of God?