Comments:

1. The first sentence is a bit too opinionated for my taste. Consider:

map(f, seq)
[f(x) for x in seq]

The map is *more* concise, by 8 chars, than the list comp and, in *my* opinion, clearer and easier to read without the extra boilerplate and extraneous dummy variable. I would write the first sentence more like:

"List comprehensions provide a concise way to create lists without having to use either a blank list followed by list.append or combinations of map, filter, and lambda expressions."

2. The added examples are nice and should help.

3. "In a list comprehension might contain arbitrary expressions, including other listcomps." is not a sentence. I think this in meant to say: "The initial expression in a list comprehension can be any arbitrary expression, including another list comprehension."

4. I completely agree with removing the scary hobgoblin stuff. In fact, I think the platitudinous next sentence "Nested list comprehensions are a powerful tool but -- like all powerful tools -- they need to be used carefully, if at all." could also go. It does not add anything not better said in what follows. Python is a powerful tool, but -- like all powerful tools -- it needs to by used carefully. Yeah, right ;-).

I believe the later sentence "To avoid apprehension when nesting list comprehensions, read from right to left." means to say "To avoid mis-apprehandion [or misunderstanding] when nesting list comprehension, read from outside in." But even this only indirectly points to what I think is the real danger -- which is to read the nested l.c. as unnested, and hence to get the order of the clauses wrong. In other words, reading
   [[f(x,y) for x in xseq] for y in yseq]
as
   [ f(x,y) for x in xseq  for y in yseq]
I initally made that mistake when reading the nested example. So I think the appropriate warning sentence should be something like:
"The main danger to avoid is reading nested comprehensions as if they were one comprehension with multiple for clauses." This could go after the revised initial sentence in place of the useless platitude.

4. The example is more confusing than need be because of using a symmetric matrix. The literal [0,1,2] is both range(len(mat)) and range(len(mat[0])) but it is only the latter that is relevant. So I strongly urge using an asymmetric matrix (3x4) and suggest using range(4) instead of [0,1,2,3]

So, change "Consider the following example of a 3x3 matrix held as a list containing three lists, one list per row::" to
"Suppose one has a 3x4 matrix implemented as a list of 3 lists of length 4::"

Change mat display accordingly, using 1 to 12.

Change "Now, if you wanted to swap rows and columns, you could use this list comprehension::" to
"The following list comprehension will transpose rows and columns."
>>> [[row[i] for row in mat] for i in range(4)]
[[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]

I think the more verbose version (slightly modified to match the below) should be followed by an even more (completely) verbose version:

trans = []
for i in range(4):
    transrow = []
    for row in mat:
        transrow.append(row[i])
    trans.append(transrow)
print(trans)

5. "In real world," should be "In the real world,".