When the jewel thief's partner is shown on screen, a German newspaper can be seen beside him. The upper and lower case formatting of the headline is incorrect.
In the beginning, a couple is suffocated. The man kicks against cardboard moving boxes which are supposedly full of household items. The kicking reveals that they are just empty or almost empty props.
The ECG electrodes on Ilya and Katarina are only loosely attached to their necks and faces. They won't work that way in real life.
It makes no sense that Reddington still should be in the dark about Liz' new "neighbour". It would mean he has completely stopped keeping any kind of tabs on her when his entire rationale for everything has always been to "keep her safe".