Whenever I assign an account, task, note, etc. to someone else other than myself, it takes about 1-3 minutes to save after clicking on the Save button. This only happens when using the Assigned to field. Assigning to myself or setting the field as empty is reasonably fast.
As far as I know, without more detailed information, this may be caused by the user profile, in Advanced separator, having the Notify on Assignment checked.
If email sending is not correctly set, having this option active will delay the save process. (maybe because the send email will timeout)