Mistakes will be made, but many pm will only compound them.  

Some of these events that have occurred recently are compounded effects from infrastructure that's worn out, more development pressure, and less greenspace. 

Its the difference between a compounded interest in simple interest.

It compounds

We have a contract, and I even emphasize to the tenant at lease signing the importance of paying on time, due to the compounding of the late fees.

Tenant had compound fracture of the leg and couldn't get to door in time.

Again not a problem but what I'm thinking is if I'm just putting 500 a month away into savings then yes I get compound interest but is there another way?

Plus, legally, if you start accepting late rent, it can be perceived by the court that you have waived your right to requiring the rent on time.Also, if your lease doesn't already include it, it should say that accepting late rent does not waive your right to demand rent on time in the future (although this is questionable as to whether or not the court would still think you waived this clause), and you should consider adding a daily amount after the initial $25, so it keeps compounding up to a limit.I used a Nolo Press contract for California, and it included a cap on the late fee of something like $250. 

Or is that inherently part of the strategy, using compounded interest, equity paydown, purchasing at the right price, rent profit savings, etc.? 

It was the compounding things that needed fixed that was surprising, especially at move-in.