Most of the time I would think that the translators do the very best that they can to make sure that the original intent of the writer of a text is transferred to the new copy. However, we all have personal bias. Even without that there are certain scriptures that have been translated in a certain way because that is what every one expects.
I will try to provide examples as I see them, but so far we have found words that have the opposite meaning in the Greek from the English presented to us in translations. We have English words that have been assigned the wrong definition. More recently we have found that, at least in the KJV, there are verbs translated as nouns, nouns as verbs, adjectives as nouns.
Below are a couple of examples where I think that the translators ignored the original for the expected translation. After all a new translation does not sell well if it does not conform to expected readings of the text. A known example of that is the word that we know as "baptism". Most know that the Greek word "baptismo" means to immerse or bury and that is how it should be translated. However, that would offend many different groups who practice a "baptism" that is foreign to the actual meaning of the word.
In Hebrews 4:1-11 in almost every verse the word rest is found. In verse 9 though the translators were at least a bit misleading by not telling us what type of rest was being mentioned as is should at the least read "sabbath rest".
Here is an example of a verb being translated as a noun. Ephesians 2:12 includes the phrase, "being aliens from the commonwealth". The actual Greek reads closer to, "having been alienated from the commonwealth". There is a difference that is very important and the English does not faithfully represent the Greek.If you have read any of the marriage related articles here then you have read the problem with the understanding of the Greek word "apoluo". In all but one verse in the new testament it is correctly translated as put away or send away meaning a physical separation. In Matthew 5:32 it is incorrectly translated as divorced, in the phrase "shall marry her that is divorced". The Greek would be more honestly understood as, "separated, not divorced". As you can see that is the opposite of the English translations.
There are more of course. As I have time I will add more.