Can we classify all the d-block elements as transition metals?
The idea that the properties of d-block elements are transitional between those of s-block and p-block elements, and that is the reason for calling them transition element is absolutely correct, but the thing is transition metals are defined is slightly different manner.

Definition of a transition metal/Criteria for an element to be a transition metal


  A transition metal is one which forms one or more stable ions which have incompletely filled d orbitals


Appreciate that the general electronic configuration for d-block elements are slightly different for those of transition metals.

EC of d-block elements: $\ce{(n-1)d^{1-10}ns^{1-2}}$
EC of transition metal/ion : $\ce{(n-1)d^{1-9}ns^{1-2}}$

Some examples of elements which are in d-block but not a transition metal


Scandium has the electronic structure $\ce{[Ar] 3d^{1} 4s^2}$. When it forms ions, it always loses the 3 outer electrons and ends up with an argon structure. The $\ce{Sc^{+3}}$ ion has no d electrons and so does not meet the definition.
Zinc has the electronic structure $\ce{[Ar] 3d^{10} 4s^2}$. When it forms ions, it always loses the two $\ce{4s}$ electrons to give a 2+ ion with the electronic structure $\ce{[Ar] 3d^{10}}$. The zinc ion has full d levels and does not meet the definition either.


There's a small thing that one must take into account that some elements are capable of forming multiple metal ions in those cases we must consider more common ion (the most stable one)


The pefect example for this case is $\ce{Cu}$ ($\ce{[Ar] 3d^{10} 4s^1}$), $\ce{Cu}$ is capable of forming two ions :


$\ce{Cu^{+1}}$ ($\ce{[Ar] 3d^{10}}$) (not the most common ion of $\ce{Cu}$)  

$\ce{Cu^{+2}}$ ($\ce{[Ar] 3d^{9}}$)  (most common ion formed by $\ce{Cu}$)

Hence, copper is definitely a transition metal because the $\ce{Cu^{+2}}$ ion has an incomplete d subshell.

Using this idea we can also say  $\ce{Zn}$, $\ce{Cd}$ and $\ce{Hg}$ are not considered as transition elements.

How are these metals different from rest of the d block elements?

$\ce{Zn}$, $\ce{Cd}$ and $\ce{Hg}$ are not hard metals (as compared to other d block elements), which can be attributed to the fact that they have no unpaired electrons which makes their metallic bonding weak.