No Way Out - S2-E13
Factual error: Gideon says that Frank is the most prolific serial killer ever, with 177 victims. This is incorrect - Pedro Lopez murdered 350+ young girls and Luis Garavito murdered 300+ plus girls.
Continuity mistake: When Garcia accesses the bank's page online Prentiss gives her the account number login, 1552 9384 6729, and we see Garcia typing it correctly on the screen with the password, but when it cuts to the account's page showing deposit and balance, we see in the balance box the account number's last four digits are 7629, not 6729.
Other mistake: In the opening scene, the UnSub is wearing breathing apparatus, however his smoke hood is under his face mask. Wearing the hood under the mask would make it impossible to get a face seal, and as such would let smoke into the mask.
Character mistake: Dr. Reid calls Penelope "Kristy" on a phone call.
Suggested correction: He calls her "Garcia."