When does it matter if a rabbi is actually a rabbi with classical semichah miMoshe vs just a chacham who went through a program, of one caliber or another(or not), and got a certification, of one caliber or another(or not)?
1 Answer
The first Siman in Choshen Mishpat details what items can be judged by un-ordained(real semicha) Rabbis ,and what can be judged by ordained Rabbis . Penalties, and unusual cases are not judged today since there isn't real semicha given .
Choshen mishpat Siman 1 -
https://en.m.wikisource.org/wiki/Translation:Shulchan_Aruch/Choshen_Mishpat/1