unfortunately, and I'm just speculating here, I don't think this phone has the greatest Exchange capabilities. I use my company's Exchange server for everything (calendar, contacts and email). The email I don't really use all that often, because I've found the "mail" app to be horribly slow (like, 30 seconds to acutally open and another 15 to show my emails). That's not a huge issue to me, since I only use that email address for work emails, and since it's a personal phone, I'm not too concerned if I miss an email while I'm away (if they wanted a leash on me, they'd give me a better device than the equivalent of the Jitterbug phone for the elderly for work). I've had no problems syncing info (contacts and calendar) with the phone and Exchange, however, I think it's calendar functions are severly limited (unless I'm missing something) as I'm experiencing the same thhing as the OP.
On my old WinMo phone, if I dismissed an appointment on the computer, the notification on the phone would disappear, and vice-versa. With the Hero, it does't seem to work that way. If I completely delete and event prior to the event's notification going off, it will delete it off the phone and never notify me, however, if the notification goes off on the phone and I either delete or dismiss it on the Exchange server via the computer, it does nothing with the notification. Additionally, there have been times where I have dismissed the notification on the phone and it re-notifies me 10 minutes later.
This, at least for me personally, is nothing more than an annoyance and if there is a setting or fix out there that I haven't seen, I'd love to hear about it. Otherwise, it's just something I can deal with, as it's not a huge deal.