Many of the so-called errors (lay vs. Iie down, If I were/was) have become so widespread that they are accepted in informal settings or in certain regions or communities of native speakers.
In fact, I have seen native tutors on italki not only frequently speak this way in their videos, but also write this way.
If one is to be careful with songs to learn English, then one also needs to proceed with caution in interactions with the majority of native speakers who frequently make these "errors" because that's just the way they speak. I am not sure that is either possible or necessary.
I have studied several languages and speak them without difficulty. Music, including popular music, has always been an invaluable resource. It is not my only source of input, but it is an important one. Learners are smart and perceptive enough to notice the differences between familiar, literary and business-appropriate language. I would argue that familiarity with different registers and the way average people speak is part of becoming a competent language speaker.
Basically, I do not see music as a significant threat, including pop and rap. I advise people to enjoy it unabashedly and see how fast their understanding and pronunciation improve.
edited for typos.