Celocanths are sarcopterygians, like us (and reptiles, for that matter). So they are more related to us than are, say, sharks, but that’s not to say they are very related. Certainly, they are no closer to us than they are to any other terrestrial vertebrate.
No, no modern species of reptile is more similar to mammals than any other.
This chart should explain: File:Traditional Reptilia.png - Wikipedia
Mammals belong on the Synapsida branch, turtles are the Testudina branch, snakes and lizards are the Lepidosauria branch, crocs are obvious, and birds are Aves.
Note that all modern reptiles are on a different branch than all modern mammals. But birds and crocodiles share a branch. Crocs are more related to birds than they are to turtles. But no currently living reptile is more closely related to mammals than any other.
People keep saying this without defining what they mean. There was a common ancestor of mammals and modern reptiles. Each mammal (humans specifically in this case) and modern reptile has a definite number of genetic changes between the moden form and that common ancestor. There is nothing unreasonable about defining the number of genetic changes as the measurement of closeness of relation. I doubt we have the means to accurately measure that, but saying all reptiles are equally related to mammals implies that all reptiles are equally related to each other, and thus not different at all. Our inablility to perform this measurement does not mean it doesn’t exist.
ETA: Not all reptiles are the same, but rather all reptiles would have an equal number of genetic changes from a common ancestor, which is not the case.
No, it doesn’t. Imagine two species of reptiles that share a common ancestor 10M years ago. Now, imagine another species that shares a common ancestor with those two 20M years ago. How are all 3 species equally related to each other, even if all reptiles are equally closely related to all mammals?
Here’s an alternate way of asking the question: What modern-day reptile is most similar to the most recent common ancestor of reptiles and mammals? Obviously, that’s going to be a difficult question to answer, partly because ‘most similar’ is a subjective measurement, and we don’t have a living example of the mammal-reptile common ancestor to study or perform genome sequencing on.
OK. I think I see what Tripolar is trying to say, but we have no way of measuring it.
Imagine three branches of your family tree from many generations ago. One branch, the Joneses, reproduce, on average, once every 30 years. The other branch, the Smiths, pop out kids on average every 20 years. You have the same branching point as both the Joneses and the Smiths, but you are more closely related to the living members of the Jones side than to the Smith side.
Yes. I assume you didn’t catch my ETA the first time. There is some hypothetically measureable difference. We may not be able to measure that difference. And simply counting the number of genetic changes doesn’t factor in the qualitative differences in those changes either. But the answer to the OP is ‘unknown’, not that that all modern reptiles are equally related to humans.
What it means is this: in order to belong to a clade, organisms possess certain shared characters. Or, to put it another way, all reptiles share certain traits, all mammals share certain traits, all amniotes share certain traits, etc. Now, once within a clade, traits will further be acquired or lost, based on the basic form and physiology of the basal populations. Derived reptiles will gain or lose traits, relative to those possessed by basal sauropsids, mammals will gain or lose traits based on those possessed by basal synapsids, and so on. Once you get past the basal forms, however, it’s all new. A crocodile’s three-and-a-half chambered heart is as derived as a marine iguana’s choice of habitat. Thus, once you get past the most basal forms of a sister branch in a clade, it becomes meaningless to talk about relative relatedness with a member of a sister branch. You can only (meaningfully) talk about what traits they all share, which means you’re really just talking about the ancestral clade.
Or, to put it in context, whatever traits any given mammal and any given reptile have in common are common with all amniotes. Thus you can’t really point to any two members of the sister branches within Amniota and say “this one is more closely related to that one than this other one”.
Modern evolutionary biologists define taxonomic relationships with reference to the last common ancestor. That is what we mean. By this definition, which is the only one generally recognized, no reptile is more closely related to mammals than any other.
The number of genetic changes is in fact used to identify clades among recent species. However, it becomes largely meaningless for more ancient relationships. Genetic changes consist not only of point mutations to base pairs, but chromosomal loss, duplication, rearrangements, etc, all of which can have profound effects. Also, some genes are highly conserved - changes are highly selected against - whereas other areas of the genome are highly variable. There is no real practical way to compare these changes over hundreds of millions of years.
As John has pointed out, some reptiles, such as crocodiles and lizards, have more recent common ancestors than others. In any case, all branches could show approximately equal changes from a common ancestor, since the changes in each branch are independent. That is, the same number of changes could have occurred in turtles, crocs, and lizards, even though the latter two are more closely related to one another.
Darn! I suppose I have to send them all Christmas cards now. 
If you choose to use clade as the measurement of relation, that would be true. But a clade is a very general grouping of characteristics that to be valid actually have a genetic basis. And genetically there is a precise number of changes between any two animals based on number of generations and changes in genetic structure. Clades do represent the qualitative changes I mentioned to John.
It’s not merely subjective, there’s no practical way to define such similarity. For example, the skull structure of turtles is similar to that of early amniotes (primitive “reptiles” in the loose sense) but the rest of their anatomy is obviously extremely different. The early amniotes were similar in general body form to some lizards, but anatomically lizards are very different.
That is how it is defined according to current practice.
In fact, the clades of reptiles and mammals do have a genetic basis. In general, to the best of my knowledge analysis has shown that all reptiles are genetically approximately equally distant from mammals; the results may differ for different genes. (I haven’t been able to locate a specific phylogeny to link to.) As I’ve pointed out, there is no “precise number of genetic changes” between any but the most recent species. The number of changes differs between genes, and between genes and other regions of the genome; and there are other changes that occur in chromosomes.
I’m not arguing any of the science of cladistics applied here. But there is a definitie number of changes between any two animals, even if we have no way to measure it. And life is not a balanced tree. All animals do not have an equal number of branches going back to common ancestors.
But that is true for individuals within the same species. So, if you want to take your argument to its logical conclusions, you would need to find the particular, individual human who was most closely related to the particular, individual reptile.
In that case, though, we all know it’s Karl Rove. 
Sure, but you cannot, based on the magnitude of the number of differences alone, even if they were measurable, infer relative relationships for very distant relatives. It may take x changes to get from Ancestral Reptile to Derived Reptile A, and y changes from AR to Derived Reptile B, but there is no universal law stating that if x < y, A is more closely related to AR than B is. Evolution does not always take the most direct genetic pathway, and those meanderings can be longer or shorter in differing lineages.
There is also no way to equate the different kinds of changes (e.g. point mutations vs chromosome alterations). Which species is more closely related to another, one that has 10 point mutations in a non-coding region, or one that has undergone a chromosomal translocation? The latter could have a much greater effect. So saying there is a particular number of changes between two forms is pretty much meaningless.
True. Generation time can make some difference to branching rate, and is sometimes taken into account in trying to estimate the time since clades have diverged.
That is correct, which why the answer can be a guess or ‘unknown’. Besides the number of changes, there is the actual lineal descendancy. But that does not make all reptiles equally related to humans.
Yes, it does.
Foul! I hadda say Goldblum to keep politics out of GQ.
(otherwise I would have scooped you on good ol’ Karl.)