You can't get the activities that have changed status the past 24h in an easy way. There is a modifiedon field which tells you when the object is changed which tells you when a record is changed, to see which field is changed you would have to query the
Audit, which should be possible but I haven't done that yet.
Use a QueryExpression (or Fetch) to find all records modified in the last 24 hours, based on the modifiedon field
Loop through the results and execute a RetrieveAttributeChangeHistoryRequest for each record to get the audit of all changes to the statecode (or statuscode)
Microsoft CRM MVP - http://mscrmuk.blogspot.com/ http://www.excitation.co.uk
If this is a really must-have feature, one way of doing it would be a datetime field that you stamp when someone changes status of the record, that would be very searchable. It will not be something you would want to implement for every field though, but
if it is just status you're looking for it shouldn't impede performance much.