It is not easy to answer your question/request as there are a lot of problems that might cause this low precision (I guess you are calculating the mAP). First, you have to make sure your code is correct, then, you have to check the data-loaders, are you loading the data correctly? I usually do this in the debug-mode, and check if everything is correct, you may also need to do some exploratory analysis on your images; for example, do some histogram statistics, visual inspection on randomly picked samples, and check if  they are correctly labeled, etc. One thing that might really be helpful to know is how much your mAP results differ from chance-level?  Have other people reported better results than yours on the same dataset? If so, there must be a  bug or more in your code or the way of doing things (algorithms), etc.
To get feedback on the multi-label classification, maybe you could post how are you doing it and maybe you will have some feedback from the forum.