Definition: something extremely good, bad, strange, big, etc.
So, if, after going to the movies, I tell you that the movie was a real doozy, I guess your answer will be "Was is it a good thing or a bad one?" Like the case of 'funny strange, or funny ha ha?'.
I searched "doozy" on online dictionaries and, frankly speaking, did not quite catch the meaning.
Webster's dictionary online defines "doozy" as "extraordinary one in its kind".
Oxford Dictionary Online defines " doozy" as "something outstanding or unique of its kind" , which is informal, chiefly North American.
I suppose a broader context might help to understand its use better.
Does doozy have high frequency in English?
I've almost always heard this word in a negative sense to be something unexpectedly overwhelming.
"That first step is a doozy"
"That math problem was a real doozy"
"Her speech was not simple, it was a real doozy"
asusena: I have heard this word more on TV comedies than in real life.
I believe "extraordinary" is the best one-word definition that has already been mentioned. It can be good or bad so context and implication are very important when this word is used. If you say a movie was a "real doozy" then more description would be required unless you are talking to a person who has also seen the movie, then the meaning can be inferred. My observation would say that its use is declining. Fifty years ago it was very commonly used in many situations but now it is probably true that it is heard more often on TV comedies. It hasn't totally died, though. In real life it is probably most frequently heard from people over 40 or 50.