The difference in pronounciation between 오 and 우, 요 and 유
When I listen to some speakers it seems to me that 오 and 우 are almost the same. Both sound like the 'o' in 'to do', or the 'ou' in 'you'. Is this an accent that is actually not correct?

For example. 보다 to me sounds like 부다. This while in for example 있어요 the 요 more clearly sounds like the 'o' of 'I go'. (Or the French 'eau', in du l'eau. Or the Spanish 'o' in dinero. Or the 'o' in the German Todesfall. If you happen to speak any of these languages.)

Should not the vowel sound in 오 and 요 always sound like the 'o' of 'I go'?

Question

The difference in pronounciation between 오 and 우, 요 and 유
When I listen to some speakers it seems to me that  오 and 우 are almost the same. Both sound like the 'o' in 'to do', or the 'ou' in 'you'. Is this an accent that is actually not correct?

For example. 보다 to me sounds like 부다. This while in for example 있어요 the 요 more clearly sounds like the 'o' of 'I go'. (Or the French 'eau', in du l'eau. Or the Spanish 'o' in dinero. Or the 'o' in the German Todesfall. If you happen to speak any of these languages.)

Should not the vowel sound in 오 and 요 always sound like the 'o' of 'I go'?

Answer

I don't speak any of the languages and only self studied korean a bit, but the difference in pronunciation between those should be very easy to distinguish:

오 = "o"
요 = "yo"
우 = "u" or "oo"
유 = "yu" or "yoo"

오 is like the o from "hello" 
우 is like the oo from "moo"
should be very easy to tell the difference between those sounds... and when you add the extra line, its like adding a "y" in front of it, so "요" should always sound like yo, such as "yo tengo etc."

Answer

While it could be some dialect differences, i would imagine that seoul dialect is the one most people would be learning, and 우 and 오 would be clear in that case. If its from a song, maybe the lyrics are too fast and it just sounds similar from another word? I'm curious what song it is and where it sounds like that now, i'd like to listen to that part. Still, in your original question, 보다 should never sound like 부다.... at least based on my 12 years of listening to korean music and watching their drama. Hopefully a native speaker responds also.