The incorrect statement among the following is :

To find the incorrect statement among the options, let us analyze each statement individually:

1. Actinoid contraction is greater for element to element than Lanthanoid contraction:
The shielding effect of 5f electrons in actinoids is poorer than that of 4f electrons in lanthanoids. Consequently, the effective nuclear charge increases more rapidly across the actinoid series than across the lanthanoid series. This results in a greater decrease in atomic and ionic sizes from element to element in actinoids, meaning actinoid contraction is indeed greater than lanthanoid contraction. Thus, this statement is correct.

2. Most of the trivalent Lanthanoid ions are colorless in the solid state:
Most trivalent lanthanoid ions
${\text{Ln}}^{3+}$
are colored both in the solid state and in aqueous solutions due to f-f electronic transitions. The absorption bands are narrow because the 4f orbitals are deeply situated within the atom and are shielded by the outer 5s and 5p orbitals from environmental effects. Only ions with configurations like
${\text{La}}^{3+}$
(f⁰),
${\text{Gd}}^{3+}$
(f⁷), and
${\text{Lu}}^{3+}$
(f¹⁴) are colorless. Therefore, the statement that most trivalent lanthanoid ions are colorless is incorrect.

3. Lanthanoids are good conductors of heat and electricity:
Lanthanoids are typical metallic elements. Like other metals, they have free mobile electrons that allow them to conduct heat and electricity efficiently. Thus, this statement is correct.

4. Actinoids are highly reactive metals, especially when finely divided:
Actinoids are highly electropositive and reactive metals. When finely divided, their surface area increases, making them extremely reactive (for example, they react rapidly with boiling water, oxygen, and acids). Thus, this statement is correct.

Therefore, the incorrect statement is "Most of the trivalent Lanthanoid ions are colorless in the solid state."