Shoots: I'm assuming you mean roots - I would remove anything that's not green or obviously in use. When I checked my rescues I had a similar situation of lots of random dry ends. Feel around - if its brittle and dry, remove it - same thing if anything is dark/black and smooshy. For the most part leave the center core alone, just trim off any icky things.
---- vendor information removed -see faqs on posting----Also when repotting - make sure you have lots of drainage and don't pack the moss/bark too tightly.
Various leaf booboos like dry spots can be trimmed off but I can't see anything major from your photo so you can just leave it be. I'm also pretty sure that as the plant is flowering on a new spike you can cut the other one back further if you like - but I'm also new to orchids so don't quote me 100% on that!
Best of luck.