In the majority of cases corrosion to the base is due to the base being left in standing water or it has been put though a dishwasher where the salts will destroy the high quality finish. The chrome will peel off the base of the ROK if it is left in damp conditions so it is necessary to wipe off any coffee or water and then dry it thoroughly. Looking at your photographs it appears the damage is on the upper side and side of the base which would be indicative of general wear and tear which would not be covered under our 10 year warranty.
You can use white vinegar to remove oxidisation/rust. This link may help: http://www.wikihow.com/Remove-Rust-from-Metal. Thereafter, fairly regular (depending upon usage) cleaning with soapy water and thorough drying. Full cleaning instructions can be found under the FAQ section of our website.
If the vinegar does not work, I would suggest trying a metal cleaner followed by a metal polish. A good hardware store should be able to help you find a suitable non-scratching cleaner.
Note that the water/coffee does not come into contact with this part of the machine during use. The passage of water through the machine touches only food grade polymers and steel and any marking is purely cosmetic.