If the 'Post Sharing' privacy of your session or sighting is set to 'Only You' then these records will not count towards challenges you have joined. Challenges are public events on Birda and are therefore only compatible with public posts shared to everyone or to a user's followers.
If you find that sightings seem to be missing from your challenges, you can add them by editing the sightings that are missing and making sure the privacy is not set to 'Everyone' or 'Followers'.
By default, your Post Sharing Privacy Settings are set to 'Everyone'. You can change your 'Post Sharing' Privacy Settings for each Sighting or Session you post or you can change your default Post Sharing Privacy Settings by navigating to your Profile > Settings > Privacy Controls > Sightings and Sessions. You are able to set you privacy to 'Everyone', 'Followers' or 'Only You'.
Location Privacy Settings on the other hand will not have an impact on how your sessions or sightings count towards challenges.