Worried about playing Batman Arkham Knight on my PS4

I bought a used Batman Arkham Knight game online and the disc was filthy af... It had dust literally stuck on the shiny side. Anyway I washed the disc using some water and soap (source Youtube) and the dust went away but there are these spots or tiny dots as well on the disc that just don't seem to go away... I was wary of putting that disc in my PS4 but I thought let's see if the game installs then the disc would only be used for verification but guess what I insert the disc and the game starts right away - no install screen or any message that the game is being installed... Also, the disc drive was making a clicking sound every couple seconds... I took out the disc right away... Now, I have a few questions... Why the hell is Batman Arkham Knight not getting installed? Will the game run from disc all the time? What should I do with the disc - use it or return it? Please help...