Let's analyze the statements:

A. The electron gain enthalpy of $\mathrm{F}$ is more negative than that of $\mathrm{Cl}$.

This statement is incorrect. The electron gain enthalpy of $\mathrm{F}$ is less negative than that of $\mathrm{Cl}$ due to its small size, which leads to increased electron-electron repulsion when an electron is added.

B. Ionization enthalpy decreases in a group of the periodic table.

This statement is correct. Ionization enthalpy generally decreases down a group of the periodic table due to the increase in atomic size, which results in a weaker attraction between the nucleus and the outermost electrons.

C. The electronegativity of an atom depends upon the atoms bonded to it.

This statement is incorrect. Electronegativity is a property of an atom that depends on the effective nuclear charge and the distance of the outermost electrons from the nucleus. While the difference in electronegativity between atoms in a bond can affect the bond's polarity, the electronegativity itself does not depend on the atoms bonded to it.

D. $\mathrm{Al}_{2} \mathrm{O}_{3}$ and $\mathrm{NO}$ are examples of amphoteric oxides.

This statement is incorrect. $\mathrm{Al}_{2} \mathrm{O}_{3}$ is an example of an amphoteric oxide, meaning it can react with both acids and bases. However, $\mathrm{NO}$ is not an amphoteric oxide; it is a neutral oxide.

Hence, the incorrect statements are A, C, and D.