1. Condition for geometrical isomerism
   A compound shows geometrical isomerism about a double bond only if each carbon of the double bond has two different groups attached.

2. Check statement (A): Propene shows geometrical isomerism
   Propene is $\mathrm{CH_3-CH=CH_2}$.

• Left double-bond carbon has groups: $\mathrm{CH_3}$ and $\mathrm{H}$
• Right double-bond carbon has groups: $\mathrm{H}$ and $\mathrm{H}$

Since one carbon has two identical groups ($\mathrm{H,H}$), geometrical isomerism is not possible.

So, (A) is incorrect.

3. Check statement (B): Trans isomer has identical atoms/groups on the opposite sides of the double bond
   This is the definition of trans isomer (for simple cis-trans systems): identical or similar reference groups are on opposite sides.

So, (B) is correct.

4. Check statement (C): Cis-but-2-ene has higher dipole moment than trans-but-2-ene
   In cis-but-2-ene, bond dipoles reinforce each other more, so net dipole moment is higher.
   In trans-but-2-ene, the dipoles cancel to a large extent, so dipole moment is lower.

So, (C) is correct.

5. Check statement (D): 2-methylbut-2-ene shows two geometrical isomers
   Structure of 2-methylbut-2-ene: $\mathrm{CH_3-C(CH_3)=CH-CH_3}$

At the left double-bond carbon, the two groups are:

• $\mathrm{CH_3}$
• $\mathrm{CH_3}$

These are identical. Hence geometrical isomerism is not possible.

So, (D) is incorrect.

6. Check statement (E): Trans-isomer has lower melting point than cis isomer
   Generally:

• cis isomer has higher dipole moment and often higher boiling point
• trans isomer is usually more symmetrical, packs better in crystal lattice, and often has higher melting point than cis isomer

Therefore the statement "trans-isomer has lower melting point than cis isomer" is generally incorrect.

So, (E) is incorrect.

7. List of incorrect statements
   Incorrect statements are: $\boxed{(A), (D), (E)}$

Thus the correct option is: $\boxed{\text{B}}$

8. Comparison with stored answer
   Stored correct answer = B
   Derived answer = B
   So, they agree.