How We're Related to Other Four Legged Vertebrates

I'm doing battle with common misconceptions in biology, a lot of which we were all taught in school and people still being taught in school.  I'm not exactly sure the level of importance of this one but I think I can handle it fairly quickly.  As always, please correct any misconceptions or feel free to argue with me in the comments.

There is a common misconception, or rather a set of misconceptions, around the relationship of the groups in Tetropoda.  Tetropoda, or the tetropods, are amphibians, mammals, reptiles (really non-avian reptiles) and birds (which are reptiles, technically).  These are the major groups that are still around today.  When you look at a lot of cladograms for these groups they look something like this:

image by me, click to embiggen

What the cladogram actually looks like is something more like this:

image by me, click to embiggen

This is a minor difference, but it's an important one and there are several misconceptions that are portrayed by the first one.  First, and I've glibly added an explosion to humans at the crown in the first one to reinforce this, it portrays evolutionary time as always going from "less advanced" to "more advanced" with us humans at the very peak of...advanced-ness.  Evolution is not a movement towards more advanced.  Natural selection doesn't have any conceptions about what is more or less advanced, only what organisms are best at getting their genes to keep going.  Just check out the bacteria.  They're the polar opposite of what most would probably call "advanced" but they're darn good at making their genes survive for billions of years (and yes, a Domain is very different from these much smaller clades).  

Second, and I may be projecting here, but I think this also portrays the misconception that amphibians "evolved into" reptiles and then reptiles "evolved into" mammals.  But if that were true, wouldn't there only be mammals?  If reptiles evolved into mammals, why are there still reptiles?  

Partly because mammals did not evolve from reptiles, rather the two groups share a common ancestor.  Millions of years ago there was a population of animals that weren't mammals or reptiles.  As this population evolved it diverged into (at least) two distinct groups.  One is what we today call mammals and the other is what we call reptiles and birds.  You'll sometimes hear people use the term "mammal-like reptiles."  There's no such thing.  There are animals that came before the common ancestor of reptiles and mammals which are neither and there are animals after that common ancestor which are one or the other (sort of, this is a bit of a simplification).  There's a group of animals called Synapsids, which mammals are a part of, and early Synapsids didn't really look or behave much like modern mammals and maybe they were kind of reptile-ish (in that they were tetropods that weren't amphibians) so we've gotten stuck in the habit of calling those animals "mammal-like reptiles" even though they're really a lot more mammal than reptile.  

Third, this also may portray the misconception that reptiles have been around longer than mammals.  So again, it gets a bit complicated, but the two lineages that have led to what we currently call "mammals" and "reptiles" have actually existed for exactly the same amount of time.  That's because they share a common ancestor, they diverged from the same population of animals millions of years ago.  So what we might recognize as a "modern mammal" didn't appear until much later, these two clades have existed alongside one another since they both evolved from a common population.  

Let me know what I got wrong, what's confusing and what you're disagree with.  This was actually a bit harder to write than I thought and I hope that my simplifications make this understandable and fairly accurate.