First of all, all consonant cause trouble for Japanese learners. All phonemes in Japanese language except one (ん) end with a vowel. Therefore, they tend to add a vowel after an English consonants. The trouble should be from speaking to listening. When they speak English, the listener may not understand them because of extra vowels. Whey they listen, they may miss many consonants because they don't consider them as phonemes but as faint noise. Regarding more specific aspects with consonants, there are some phonemes which are difficult for them. For example, I can list /f/, /v/, /θ/, /ð/, and /ʃ/. These phonemes are what Japanese language doesn't have. Therefore, Japanese learners pronounce /h/ instead of /f/, /b/ instead of /v/, /s/ instead of /θ/, /z/ instead of /ð/, and /s/ instead /ʃ/. As another example, I can list /r/, /l/, /m/, /n/, /ŋ/. These phonemes are what Japanese language has similar phonemes to, but these Japanese phonemes are also similar to other English phonemes. In other words, one sound in Japanese can become two or more sounds in English. "ら" is similar to both /rʌ/ and /lʌ/ but not exactly the same as either. "ん" is pronounced sometimes as /m/, sometimes as /n/, and sometimes as /ŋ/. That depends on which phoneme is following "ん", but as a matter of fact, we don't care about it and just consider as one phoneme. That troublesome similarity cause that Japanese learners are confused between /r/ and /l/ and between /m/, /n/, and /ŋ/.
In terms of vowels, there are also some problems. Since Japanese language have only 5 vowels, Japanese learners can't distinguish each vowel easily. For example, "あ" is similar to /ɒ/, /æ/, and /ʌ/. Therefore, they usually pronounce "hot", "hat", and "hut" in the same way. Also Japanese language doesn't have 'tricky vowels' as English language has. Here I define that 'tricky vowels' means glided vowels, diphthongs, and the r-vowel which consists of /ə/ and /r/. Without knowing the existence of these vowels, how could Japanese learners possibly pronounce "caught", "coat", and "court"?
To solve these problems, I will use phonemic symbols. For Japanese people, it's unusual that there is no letter that expresses the sound. We pronounce words as they are written. To accustom the students to English spelling, teachers should teach phonemic symbols first. After that, I will use some words and sentences, which include the target phoneme. Also I will often use minimal pairs to make sure that they can distinguish phonemes. However, I suppose that learners before reaching puberty can get accurate pronunciation unconsciously and are possible to be native-like. Therefore, this method is for learners over the age of puberty. That should be during junior high school or after.