Settings -> Error notifications -> Sound -> No Sound
That is self-explanatory, - for errors.
Other places for other notifications:
Settings -> Send Notifications (I believe it is disabled by default, but you can verify)
Settings -> Message Notifications (I assume you've done those)
Also, long-press on the account in the account-list view -> Special Settings -"Message notifications" and "Send Notifications" (Both are disabled by default, but if you've changed, you can change it back to disable.)