On the way adiabatic processes were defined in Blundell's Concepts in Thermal Physics In Blundell's Concepts in Thermal Physics, page $117$, the author defines an adiabatic expansion as follows,

The word adiathermal means ‘without flow of heat’. A system bounded by adiathermal walls is said to be thermally isolated. Any work done on such a system produces an adiathermal change. We define a change to be adiabatic if it is both adiathermal and reversible.

On the other hand, this Wikipedia article clearly specifies that in order for an adiabatic process to happen, the expansion/compression must happen relatively fast. But Blundell's definition for an adiabatic process incorporates the condition of reversibility, which requires the process to happen infinitly slowly. The wiki article didn't add the reversibilty condition in its definition.
Is Blundell's definition incorrect?
 A: It's important to distinguish between several things:


*

*A process which does not change the entropy

*A process which involves no transfer of heat

*A reversible process


Blundell is correct in that (2) and (3) together imply (1). However, conventions differ on whether (2) is called adiabatic, or (1) is called adiabatic. When you're doing more sophisticated thermodynamics, it's more useful to call (1) adiabatic, because the entropy is so important. However, in high school you'll often see the definition (2) used, mostly because irreversible processes are barely mentioned at all, so (1) and (2) end up being equivalent. It goes without saying that neither definition is "wrong", it's just a different way of using words.
Under definition (1), statements that adiabatic processes are "slow" and "fast" are simultaneously correct. They have to be much faster than isothermal processes, as otherwise heat transfer would become significant. But they also have to be much slower than processes like free expansion, which would be irreversible. It would probably be better to say that adiabatic processes are neither very slow nor very fast.
A: There are a few points to address here.
First, I would hesitate to say that a definition can be "incorrect" in the first place. Definitions are, in a sense, conventions, especially when it comes to terminology. A definition can certainly be unclear, or self-contradictory, or inconsistent with later usage, and in those cases you could certainly say that a definition is poorly-chosen, but the fact that what Author A means by a term is not the same thing as what other authors mean does not indicate that Author A's definition is incorrect. As long as Author A explicitly clarifies what is meant by the terms they use in the works they use, and as long as Author A uses their terms in a self-consistent manner, there is nothing incorrect about their work, and the only thing that can be said is: "This author uses a different definition for these terms than the majority of other authors."
You can see a similar situation in many electromagnetism textbooks: some authors define the magnetic field to be the vector field $\mathbf{B}$, while other authors (usually older textbooks, in this case) prefer to define the magnetic field as the vector field $\mathbf{H}$. Neither convention is incorrect, and as long as you pay attention to the definitions outlined in the work you're reading, you'll usually avoid confusion.
Second, adiabatic processes do not have to be "relatively fast", or at the very least, the meaning of "relatively fast" can encompass processes that are usually considered very slow. The defining condition for (the usual definition of) an adiabatic process (i.e. what Blundell calls an "adiathermal process") is that no heat enters or leaves the system. If you have a system that's totally isolated from its environment (like a container with ideal-insulator walls, or the entire universe), then an adiabatic process can occur as slowly as you like. In non-ideal situations, this translates to the following rule: A process is well-approximated as adiabatic if the time taken for the process to occur is small compared to the rate of heat transfer to the surroundings. If your container is well-insulated, then slow processes can be adiabatic too.
Blundell's definition of an "adiabatic" process is equivalent to the usual definition of an isentropic process, which is a reversible adiabatic process (and therefore one that preserves entropy).
A: 
The word adiathermal means ‘without flow of heat’. A system bounded by
  adiathermal walls is said to be thermally isolated. Any work done on
  such a system produces an adiathermal change. We define a change to be
  adiabatic if it is both adiathermal and reversible.

I disagree with the statement that a change is an adiabatic change if it is both adiathermal and reversible in that it implies the change has to be reversible to be adiabatic. An adiabatic process can be reversible or irreversible. If the process is both adiathermal and reversible, it is then called an isentropic process, meaning it is a constant entropy process. 
What's more the use of adiathermal walls is a sufficient but not necessary condition for a process to be adiabatic. As Wikipedia points out a process that is carried out so fast that there is no time for heat to transfer is also an adiabatic process. However, such a process is inherently an irreversible adiabatic process because a reversible process has to be carried out extremely slowly (quasi-statically).
Bottom line: Blundell is misleading in implying that an adiabatic process has to be both adiathermic and reversible. It can also be irreversible. It is also misleading in that it suggests adiathermal walls are required for a process to be adiabatic. A process can be carried out without adiathermal walls so fast that it is in effect an adiabatic process.
Hope this helps.
