Why won't my iPhone won't take photos in landscape mode

This is problem that's vexxed me for a while. I'm on a 5s with everything up to date. I open the camera app to take photos, and I rotate the phone so I can take photos in landscape view. I take some photos, no problem.

However, when I go to view the photos in the photo app, the photos are displayed in portrait mode, rotated 90 degrees. If I physically rotate the phone 90 degrees, the screen rotates too, so that I can never view the photo as it was actually taken. The only workaround it to lock the screen orientation (I normally leave it unlocked) or edit each photo to rotate them 90 degrees. Either way is a pain.

More curiously, this problem is not occurring 100% of the time. Last night I took 8-9 photos of my girls. The first two came out "normal." The remainder (taken about 60 second later), suffer from the problem described above.

What am I doing wrong?