When Liz tells the task force Tolliver is her mother, not one member asks her how she knows that and how she has confirmed that fact to be true. They all take it on faith with zero evidence, same as Liz.
Reddington says he was on his way to "Kowloon City." Someone as well traveled as Reddington would know it's simply called "Kowloon." And, he mispronounces the name of the old airport as Kai "Talk" rather than Kai "Tack."
It makes no sense for Liz simply to ask Rostova/Tolliver directly for "the truth" when she has so little knowledge and barely any evidence. She has no way to know whether any of what Rostova says is true. As a rule, law enforcement will not ask suspects questions they do not already know the answers to. It does not even make sense for Liz to pretend to believe her and take everything Tolliver says in that lengthy exposition dump on faith.
It makes no sense for Liz to only start worrying about how Tolliver/Rostova is planning to extract the information from Dominic and if he might be in danger after she has already delivered Dom to her.
It makes no sense for Ressler to straight up ask Liz if she can be trusted. What does this law enforcement officer expect her to say if she is not trustworthy? If he has any doubts, he should go to their superior, AD Cooper.
It makes no sense for Cooper to leave Liz on duty after she tells him that Tolliver is her mother. She has a clear conflict of interest and given her past disloyalty, he should not just have suspended her but put her in custody for the duration.