There is a rectangular-shaped anomaly behind the upper portion of the 3. I don't know exactly what process would have created it. Any ideas?
No idea, there's about 8 known double die reverses and repunched mintmarks for 1935 between the P, D and S mints, whats the reverse of this coin? Nothing is known for the obverse of 1935 that I'm aware of.
Wexler shows 1 obverse doubled die listing each for the (p) and s. The s listing included the date but it doesn't look like yours