If a child says he sees ghosts, is that a reason suspect a mental problem?

No. Kids often say this. If he is otherwise normal. Iwould not worry about it.
No she/he may be . intuitively gifted. If you are open to the idea,the child is in good hands. If not, find a child someone comfortable talking with them about ghosts and see what comes up. Are the thinking of a dead relative, or see ghosts in their home only. Find out if there is a reason to believe your child before dismissing them. i saw spirits as a child. My dad believed me. That was helpful. .