If I see any merchandise out of place, I fix it.
or should it be ...I fix them.
"Any" is just a modifier for this purpose - the number of the noun it modifies is unchanged:
If I see any merchandise out of place, I'll fix it. (mass noun)
If I see any item out of place, I'll fix it. (singular noun)
If I see any items out of place, I'll fix them. (plural noun)
"Any" is neither singular nor plural - it means "one or more [optionally: of the following] things."
Any car that hits that pothole will suffer tire damage.
or
Any moths that see the light are irresistibly drawn to it.
But "merchandise" (in your example) is singular.