In season 2 of A Series of Unfortunate Events, it's revealed that Count Olaf apparently knew,
in the season finale, that 'Beverly', 'Elliot' and the half-wolf baby were the Baudelaires in disguise
In a world where such information is often difficult* to know, how did Count Olaf know?
Olaf inferred from the Heimlich hospital tag that the Baudelaires had come.
Olaf's discovery that the current Madame Lulu was the librarian Olivia Caliban led to his realisation about the Baudelaires.
Olaf knew from the beginning because he actually has a knack for seeing through disguises as seen in the Heimlich hospital arc where he saw through Klaus' disguise as Dr Faustus.
Olaf already knew that the Baudelaires got in the trunk.
Esme discovered the Baudelaires and told Olaf.
It's at least one of the above and then additionally, VFD people have a knack for seeing through disguises. Add-additionally, Olaf disguises himself often and thus (so, there's a one-way implication between practicing and recognising?) sees through disguises.
I think it's not 3 or 4 because
of the way Olaf reacted to the Heimlich hospital tag.
*'Difficult' here is a word which is used to avoid spoilers. I mean that...
...it is 'difficult' to see through disguises because adults are stupid or disguises are somehow that good or that good to fool adults. Thus, it is a wonder that Olaf saw through the disguise. This is kind of like how, iirc, the Alethiometer from His Dark Materials wasn't accessible to the protagonist after a certain point because of age.**
**ETA re His Dark Materials: Apparently, it wasn't because of age. Fine. We can try an example from Kids Next Door or Harry Potter if you want. Pick any scifi or fantasy show where that has an age maximum rather than age minimum on something.