This is a business and you should treat it as such. Don't stray away from the policies that you should already have in place regardless of if the tenant pays on time or not. If you "let things slide" you are setting a precedent with your tenants and they will expect it the next time.
If the tenant damages something and lets me know, or I see it during an inspection; it's getting repaired and billed now. Otherwise you're holding less of a security deposit come lease termination.
I have a clause in my lease that anything under $75 to fix is the tenant's responsibility.
Yes, we have "shown grace" for single instances for long term tenants -- but we never do it without letting the tenant know we are doing him/her/ze a favor this ONE time. The key is letting the tenant know you know about the damage or violation and are not afraid to address it. That way you stay off that slippery slope!