You need to keep in mind that TSPP has a light colored playfield. There are different colored TSPP playfields, but from your pics, yours looks very bright. I'd guess it's not a first run playfield. Ball trails will show up quick on light colored playfields. No way to avoid that. POTC is another one.
And even on a brand new game, dirt happens. You can't clean all the dirt away because it will come right back. Even HEP games get ball trails. White rubbers and bright post sleeves (neither are factory) are magnets for dirt, as are urethane flipper rubbers. It's somewhat ironic that bling attracts dirt. You wanna look good, you gotta get dirty.
I operated my TSPP and whenever I had the glass off, I cleaned the upper playfield. A dirty upper playfield eventually makes the couch shot impossible. I also kept the upper flipper rubbers clean (along with the 3 lower flipper rubbers). The rest of the rubber rings occasionally got cleaned. Lower playfield got cleaned after the upper and not as meticulously. Keep your upper playfield clean and don't sweat small ball trails and smudged posts on the lower playfield. It's an epic game that takes many hours to explore. Don't waste too much time cleaning.