Is there such a thing as "Over-pronouncing" a consonant?

I've only started to learn Korean from Memrise, and I noticed that some words, and it seems inconsistent at times, begin with a different pronunciation from how it's written. I wonder if I'm just not hearing them correctly because of how subtle they are... An example was, when I was in high school, I asked a Korean classmate what "Nara" meant, and I was absolutely unaware that when Koreans say it, it sounds like "ndara/dara", it didn't seem like a giant issue.

I understand that languages have their quirks, like how the "Th" in "The" doesn't sound like the "Th" in "Thought", but then my concern is, in order to be safe, would it be incorrect to pronounce the "G" sound for ㄱ and "K" sound for ㅋ as a matter of clarity, or is it necessary to really train oneself in not "over-pronouncing" these consonants or else risk being like a Korean analogue to Elmer Fudd?

The easiest of these consonant for me is ㄹ and ㅅ because they resemble the Japanese equivalents.

What are some of the pronunciation errors that tends to be noticeable from non-native speakers?