Japanese and English aren't even related languages, so their grammar is completely different, to the point where the way you would say something in one language is literally impossible in another.
For example, Japanese is a very contextual language. There is very little in the way of pronouns, subjects are often omitted entirely, gender is often ambiguous, and so forth. I've even seen a spoiler in the English translation of Pandora Hearts, where the Japanese language could be purposefully ambiguous by omission, but the English, by grammar necessity, revealed the identity of a particular person from the get-go. Though perhaps a less literal translator could have avoided that trap.
Another difference that causes translators alot of pain is keigo, or formal Japanese. Japanese makes very rigid distinctions in what kind of language you use when you are speaking to a subordinate, a superior, or a peer, and it just does not come across in English, most of the time.
Even simple nouns between languages of course don't have a consistent meaning, yet a common mistake many translators will make is to assume they do. For example, the word hoshi can mean planet or star, but many people very consistently only translate it as star, even when the text is obviously talking about a planet.
Good translations also frequently require culture knowledge that the translator may or may not have. Occasionally I've seen mistakes in translations simply because the translator was not up to date on pop culture knowledge, for instance -- I recently saw a mistranslation that "dere" is short for "tsundere" because the translator was unaware that tsundere is a slang word made by compounding the sound effects for a disdainful "hmph" (tsun) and flirting (dere.)
Furthermore, there are some translations out there that are flat out terrible. Ones in particular I remember are the official subs for the streams of Full Metal Panic and Beast Player Erin, both had obvious mistakes left and right. Bodacious Space Pirates, the sub for the stream, also consistently mistranslated suna no akahoshi as Sand of the Red Star when it literally just means Red Planet of Sand or just Sandy Red Planet (yet another mistranslation of hoshi, plus just flat out misunderstanding the function of "no" in that phrase.)
On the whole though, I'd say the quality of translations these days is generally at least serviceable, but you still would probably get more out of it if you understand the original language.