I don't know if this is just because I have the trial version, but:

On BerryBuzz, as soon as I open my screen or click anything, even if I am not clicking the message, the LED light stops flashing.
This is a problem for me because sometimes I leave a message even when I go on the blackberry and I like the LED light to continue flashing.

Is there any solution to this? Is it just because I am on the trial version?

Go over to Bellshare.com/forum and I think you'll find an answer.

With Bellshare software trial versions are identical to purchased versions - no functionality is removed - they work only for 7 days and then stop unless you have purchased an unlock key.

The chances are your trial version is version 1 but there's a new version in beta - version 2. You may want to wait for version 2 before you buy - it really has a ton of new features and I believe will release in the next few days.

In version 2 for most reminders - messages as an example - you now must actually open Messages before the reminder will be turned off. For others (missed call for example) it still works this way because of API limitations.

There is always the option of re-installing the trial version...may not fix the issue, but it can't hurt...

a new version is being beta tested now - coming soon

I'd post over on their forums, or try to get into their private beta BerryBuzz 2.0
(I haven't gotten into their beta yet :( probably won't either lol...)

Actually the new version (2.0.64) has now been released, and users can select what cancels a message reminder. One option is on the first trackball or keyboard activity (as describes by the OP) - this may be desired by users with a pop-up app or a theme that shows new messages without actually opening the message app - and the second option requires actually opening (and on some devices like my 8900 - closing) the message app for those who may want to do certain things on the device without losing the reminder for new messages.

There is always this option... but I recently discovered (the hard way) that removing the app also will delete any custom profiles you may have built. I lost three profiles that I had built for work paging, etc... had to recreate from scratch... grrr I hate it when app do that.