After playing a while with the phonetics flash site I've discover that I am pretty OK regarding consonants
Vowels instead are a big issue for me, I can not distinguish and surely can not produce more than 5 or 6 when theoretically English has 12.
I guess this is a problem for Japanese also as they has only 5 different vowels sounds.

Also, the word to IPA SRSing or at very least shadowing may be a good idea. Lots of words I never really learned the correct pronunciation and keep saying them as I may like.
For instance, yesterday I kept using the word "messiah" in a conversation, pronouncing it like /mesia/ when in fact is similar to /mesaia/ ( dictionary writes /mə'saɪə/)

Are you a native English speaker? That would be pretty helpful to know.

My father taught me to read English through alpha phonics. I wonder if that would help.

That I am not a native speaker is the main point of this thread