The 1N457 is a low leakage (non-gold doped) signal diode. A small signal transistor collector-base junction can replace the 1N457, but a 1N4001 or 1N4148 will work fine in this case. Any leakage will flow through R2+R3 to create an error in the output voltage.
The diode allows switching between constant voltage and constant current mode. In constant current mode, the operational amplifier pulls the adjustment pin of the regulator low to control the output current. Once the current is low enough, the output of the operational amplifier swings high and the diode disconnects it from the adjustment pin so the regulator enters constant voltage mode.