Notifications for new answers are quite easy. Here's what I did for StackAppletStackApplet:
- Grab the users' recent 100 questions (the maximum) with no body or anything
- Combine the IDs using ';' and make the following query:
http:// {site} /1.1/questions/ {combined_question_ids} / answers?fromdate= {time_of_last_poll}
What this is essentially doing is grabbing all answers posted since the last query for the 100 question IDs provided. This will catch 99% of all new answers.