I actually just fielded the answer to a question about this from a manager.
I'm glad you aren't dealing with hourly employees on this.
The most disturbing thing to me is item 4, particularly if it happens within the same department. If one department awards it and another does not and they are respectively consistent about that all the time, it's less of a problem but still a pain to manage. Either way, that issue brings up Fair Pay Act issues and concerns about discrimination. That, in and of itself, should give you significant leverage to address this, if that is what's going on.
We do not allow comp time here at all, although the request for it comes up from time to time.
In theory, having people work less one day because they worked more on some other day goes against the very idea of the salary basis of pay because it is a back door methodology for paying based on hours worked rather than on goal attainment. At the same time, from a practical standbpoint, managers want to be able to reward people for staying at work until 11:00 PM working on a proposal or for working 2 shifts because the night person on the other shift in a critical role is out ill that day.
There are sort of three paths you can take on this. One is to say that bonus time, granted in increments of full days only, is based on the number of hours worked in a work week. However, that pretty much entails the need for someone to document that the threshold has been met. If you want to try to kill it, push for having salaried people clock in and out and express concerns about Fair Pay Act and discrimination wiggling its way into your organization. Salaried people normally don't like to use time clocks, so that may kill it right there. If you want to be more accomodating, create a form that has the required information on it for the supervisor to fill out rather than asking them to write some sort of open ended memo. The form can always have plenty of open ended explanation space, but having the manager document the employee's hours worked on a day-by-day basis would probably minimize the desire to throw comp time around. The third method, and the one that will be easiest for everyone but also open the door to more comp time being granted is to come up with a program that allows a manager to award bonus vacation time for "going above and beyond" and have them explain how the employee went "above and beyond" (this is back to the memo idea) and start keeping track of the reasons given and the awards granted. Eventually, standards will come out on their own or you will be able to set some based on established practice and they should be pretty much in keeping with the culture of your company.
One thing that usually contributes to a situation like this is a lack of direction from above. Perhaps HR should negotiate with business leaders at a higher level to decide if they even want this going on. In a small to medium company, I would think that you would want to know that the CFO is aware of the practice because he or she will probably want a program that is measurable if he or she will even allow it to continue. In a larger company, push it up the ladder to be dealt with at a true decision making level.