Delete Dropbox

have you quit dropbox?

when you click on the dropbox icon in the titlebar clicked on the v most right in the dialog and clicked Quit Dropbox

if you have have you attempted to open Activity Monitor and terminated

Dropbox and DropBox Finder Extension ?

I was able to stop the "extension being used" by going to Applications> Utilities> Activity Monitor> click on DROPBOX in the list then hit the "X" top left. I had to force quit it, I was the FINALLY able to TRASH the app from Applications folder.

Also, if you first go to "GO" at top of mac window. GO> Find Folder> type in ~/.dropbox (squiggly line + backslash + dot + dropbox) then drag to trash. Once again goto GO> Find Folder> type in /library (backslash + Library) and delete Dropox there as well.

Safe Boot from the HD, (holding Shift key down at startup), does the problem occur in Safe Mode?