"Several flights per year" end up flying in alternate law.
The most common cause for that is either manual disconnection of 2 ADRs (there's even an airbus procedure recommending this in some specific cases), or the freezing/loss of two (I think) pitot or static or aoa probes.
New question tonight : do you think the ambiant noise could have told the AF447 crew that they were at a slow speed rather than a high speed ?
The copilot thought they were fast. Maybe that was due to unusual noise, because of the wierd airflow around the airplane ?