It is not only a question of a personal mistake OR a dogmatic definition. There are magisterial statements which fall in between and require the assent of Catholics, even though they may not be infallible dogmas.
A magisterial statement which is not intended as doctrine or dogma does not fall under the notion of infallibility.
Could a Pope make a statement, not intended as doctrine or dogma, which is in error? Asked and answered: yes.
Have there been personal mistakes made by Popes in any of the official papal encyclicals written throughout the history of the Catholic Church
Not every word in a papal document is a statement of doctrine or dogma. Therefore, by definition, not every word in a papal document is protected by infallibility.
, or are Catholics required to take these official encyclicals as teachings to which they must adhere?
Now you’ve moved on to a different question. Earlier, you were asking about assent to doctrine and dogma. Now, you’re asking about assent to assertions that are neither doctrinal nor dogmatic. Yes, there are teachings which fall outside these categories. Yes, Catholics are called to obey the teachings found in encyclicals, even if they’re not, strictly speaking, ex cathedra statements.
Are Catholics required to assent to the teachings given by Catholic Popes at Ecumenical Councils or can they simply write these teachings off as personal mistakes? I thought that Catholics are required to assent to magisterial documents of the Catholic Church.
Correct.
Even if the statements aren’t intended as ‘irreformable’, Catholics are to assent to them.
I don’t think that you can legitimately write it off as just a personal mistake of a Pope if he says in an official capacity that Jews can or cannot be saved.
It would be important to look at the statement in context, in order to discern what exactly was being said.
