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Hilbert presented ten of his 23 problems at the Paris conference of the International Congress of Mathematicians, speaking on August 8 in the Sorbonne 1900.
In which of the 23 or 24 problems was rating (as he was speaking about actual mathematical problems he made estimations about their solvableness etc.) totally wrong and if it is possible to explain, why?
Contrary to what you say, Hilbert very rarely says anything which can be interpreted as a "rating".
There is no objective criterion to "rate" the problems except by the time it took to solve them.
Some problems were solved even before Hilbert stated them, for example, problem 3. Problem 22 (uniformization) was solved (in dimension 1) in 1906.
Problem 7 was rated by Hilbert as very difficult. It was solved in 1935. On the other hand, Hilbert was optimistic about problem 8 (Riemann hypothesis), which is understandable because there was a recent breakthrough at that time.
In some cases Hilbert was wrong on the answers: For example, problem 2 was "to prove that axioms of arithmetic are consistent". This is impossible to prove, as Godel showed in 1936.
Many of the problems were not specific questions but wide research programs. So one cannot really say whether they are solved or not.
EDIT. I asked Gerry Myerson about his answer mentioned in KCd's comment. The information comes from the book of C. Reid, Hilbert. In it Hilbert's talk in 1920s is mentioned where he gave this assessment of the three problems. His opinion about Fermat's problem was right. Only the comparison of the Riemann problem and transcendence problem turned out to be "wrong". I suspect that majority of mathematicians would agree with Hilbert's rating of these two problems at that time.
