I think the red i circle is just the "Info" icon that you can click to view details about that specific calendar. If you open the Phone app and view Recents, each entry has a blue i circle next to it that you can touch to open details about the call.
Have you tested the syncing function from the phone to Exchange? It might be interesting to see if an event created using the phone's Calendar app will immediately sync to Exchange.
Other potential factors:
Are the users syncing Public or Published calendars, Shared calendars, or Sub-calendars? If the user doesn't have Owner permissions to the master calendar and all subcalendars, or if the user's calendar was set up as a Public folder or Published to the web, then syncing might get a little wacky.
Are the events that get "stuck" created by an account delegate, or added to the user's calendar by someone who is not the account holder or a delegate?
Are the non-syncing events invites that were emailed to the user? Were created as "Meetings" instead of "Appointments" or vice versa? Are they all recurring or all-day events? Is it only happening for calendar items added via the Web app, or Outlook, or third-party calendar? I don't know why any of that would matter, but if you can narrow down the issue to a specific type of record, then it might be easier to Google for a solution.
Maybe the events were added during a time when the user was on Offline Access, and it's taking a while for the event to synch. Or maybe the phone is only set up to sync events in a certain time frame and the event date excludes it from syncing.
Long shot: In Outlook - Calendar - Calendar Permissions/Properties, there is a Synchronization tab with a Filters button. If there is anything set up there, it will affect how calendar items sync.
Looking over this list, it might be easier to just delete and re-connect the Exchange account every time it gets cranky. Good luck!