I recently inherited some multifamily property and the longtime property manager has leases set up with many different due dates. About half are due on the 1st, some on the 15th, some in the 20s, etc. The main reasoning behind this is that many of the tenants are in various situations (govt. payments, etc) where they only get paid once a month somewhere in the middle of the month.
Looking back at the past year of bank statements it appears that all the scheduled rent is being collected, no payments are being missed (and when they are, they get evicted in a timely manner). So it seems like this arrangement works out fine for the property manager. He doesn't complain about it, although it seems like insanity to me, having to constantly be thinking about which rents are due every week of the month.
Part of me thinks if it ain't broke don't fix it--it seems to be fine with PM and the rent is all being collected--but another part thinks it's terribly inefficient. There's an interesting discussion that touches on this topic at Why is Rent Due on the First of the Month? Does anybody else have experience with this kind of setup, and how does/did it work for you?