From my experience, I believe that the controversies stem from the parents more than the coaches based upon previous exceptions that have been made. Here are my thoughts on the questions you have raised:
1. All wrestlers should be required to weigh-in wearing a singlet. You have to wrestle in them, why not where them to weigh-ins?
2. Weight Allowances: Rule 4-5-4 states "There shall be no weight allowances, unless otherwise allowed by the tournament director." However, it is modified for the state tournament to "There shall be no weight allowances given." One way to eliminate the controversy is to simply just follow it and quit making exceptions!
3. Late Weigh-Ins: Times for weigh-ins are posted for a reason. I understand the "bad weather" exception, especially with this last week of weather, but it should never be extended so long for this reason that it delays the entire tournament for the rest of the wrestlers and their families who planned appropriately to arrive on time. But, if the weather is that bad should you really be risking the life of your family rushing to make weigh-in for a tournament?
4. Challenge the scales: I have seen several tournaments when this question arised allow wrestlers to weigh-in on other scales that are available at the weigh-in in order to check the consistency of the scales. An easy way to find out if this is a problem is to check the scales prior to weigh-ins to see if any potential problems might be incountered. If so, you will know ahead of time and will be able to act appropriately when a question of weight is raised.
We all have to remember that the weight classifications are set for a reason and once everyone follows it, I believe that the controversies will become limited once the standards are set.