Third section.
Response to True origins.
true origins paper #1
The Overselling of Whale Evolution
http://www.trueorigin.org/whales.asp
Mesonychids to Archaeocetes
I would agree here, from what I've seen there isn't a solid amount of fossils for the whale-mesonychid connection, especially since DNA evidence suggests they split from the mesonychids early than they thought. Of course mesonychids are generally considered a run up to the start of the whale transitionals (starting with Pakicetus) so there really isn't much to talk about here.
Amphibious Archaeocete to Fully Marine Archaeocete
The main argument they use is the exact dating of whale fossils. Ironically they have half the answer on their site but seem to ignore it.
"It is important to understand that, in calling these creatures a series of transitional fossils, the evolutionist does not mean that they form an actual lineage of ancestors and descendants.* On the contrary, they readily acknowledge that these archaeocetes cannot be strung in procession from ancestor to descendant in a scala naturae.[17 ]"
The transitional fossil set of whales may not be a direct lineage and evolution is best described as a branching tree or bush, one species doesn't always turn completely into another but many branchings happen.
It is quite possible that one species split off of the earlier one and both continued at the same time. So fossil finds could over lap but that doesn't pose a problem. Dating is also not an exact method and gives a margin of error which would effect the accuracy of the claim that these fossils are being found close together. Unfortunately no solid data is given.
Indeed, the tremendous size difference between Basilosaurinae and protocetids casts doubt on that hypothesis.* All protocetids were less than ten feet long, whereas Basilosaurus cetoides was over 80 feet in length, and Basilosaurus isis was over 50 feet.[27]* It has been calculated that, even in a rapidly evolving line, changes in size are usually on the order of only 1-10% per million years.[28]
Most people tend to forget dorudons which lived at the same time and were much smaller but share similar characteristics. What is also often ignored are the two tiny legs still present on the basilosaurus. Basilosaurus is thought to be one of the first wide spread whales.
I would doubt the growth numbers were meant to be taken as solid fact by Mayr. Without further details I would also doubt they have much baring on an aquatic animal who's size has been slowly increasing. Being one of the first fully aquatic whales, factors that limit size on land no longer apply and the whale can get as big as the environment will allow. In the water being larger can also protect against attacks.
Archaeocetes to Modern Cetaceans
They start out with a quote from 1945 and another from 1965 to show that experts don't think archaeoceti are directly related to modern whales. You would think that if that is still true today it would be possible to find some new quotes, unless zero new evidence has been found, and we know that isn't the case. They answer their own problem, "The current leaders in the field believe that archaeocetes were ancestral to modern whales, but there is no agreement on which family of archaeocetes was involved."
It is common for scientists to not agree on the direct lineage. The problem is that we just don't have enough evidence to get an easy fix on the details. However, the scientists are arguing the details and not whether or not there is a clear transition.
Conclusion
There seems to be nothing here refuting the whale evolution, only questioning how exact the details are.