In most places a landlord can only do inspections every 6 months to a year and if the landlord is doing monthly inspections they are likely doing so illegally.
You should speak with your landlord about the excessive inspections and research your local landlord and tenant laws because the landlord and tenant laws can vary from state to state.
But usually monthly inspections are considered illegal and excessive by some courts and you could likely get the monthly inspections stopped even if it's spelled out in your lease.
Before the apartment or dwelling inspection can happen the landlord must always legally give 24 or 48 hours notice in advance of the inspection.
The landlord cannot just show up unannounced and do the inspection.
If the landlord is wanting to do monthly inspections it's likely the landlord has had problems with previous tenants destroying the property.
However monthly inspections would always be considered excessive and I would not want that either.