Headphones

There's few songs I like that became less enjoyable when I got "better" headphones with more detail. I started to notice issues with the recordings that I can't unhear now. I even though the headphones were broken and distorting but I tried different headphones and different sources and once I look for those flaws they become very obvious. One example is "Fever" by Eva Cassidy where I hear distortion around 0:50 in the right channel. Another one is "Summer in the City" by Joe Cocker at 3:06, crackling sound also right channel. Am I going crazy? I can't stop noticing this even after switching back to my old gear.