I've been on the board in my builiding for over 15 years. We're on our 4th mgmt co, not counting a merger. After about 20 agents, 3 or 4 were worth the money. The rest had trouble writing a decent letter, doing a weekly walk through of the building, staying on top of the required inspections, filings, etc. We're going through a second bout of late elevator inspections with hefty fines. Typical follow up of issues presented during a board meeting occurs 2 or 3 days before the next meeting, resulting in a continued list of unresolved items. I spend several hours a week myself talking to contractors, reviewing tasks with building staff, checking for new finance dept charges, violations, water meter charges, etc. to try to avoid late fees, etc. when the bills get lost.
Insurance proposals came in 4 days before current policy expired. All you can do is keep a checklist of things that they need to do and follow up to make sure that they are done timely. Know who the back office staff is that handles your building, deal with them directly if you can, copy in your manager on emails, scan/copy/date everything you send to them.