If your Dropbox seems to continuously say it's busy syncing, or does not appear to be syncing all your files, try quitting and restarting Dropbox to resume syncing.
You can quit the Dropbox app by right-clicking the Dropbox icon in your menu bar or system tray. Select the gear icon and click Quit Dropbox. Then relaunch the Dropbox app to resume the sync.
For more information on this particular issue, please see this Dropbox article.