Hi John,
I wish I had a quid for every time this one came up.
Basically you have to use abrahive liquids to polish out the scratches.
Using small circles( similar to what the Sgt Major told you to do with your boots) you cover the whole surface of the window and in doing so the scratches will disappear.
What kind of abrasive is up to you. Start off with a mild one such as T Cut on a small area of your least noticable window. If that removes the scratches, do the rest of that window with T Cut. If that isnt strong enough use something a little stronger like metal polish. If by using Tcut you are left with a serier of small circle in the reflection, then continue with a less abrasive polish such as car polish. Its better to start with an abrasive that is only just strong enough and work finer than to go at it with a really strong polish and have to work your way to smoothness. There are some proprietary brands on the market and from my experience they are quite powerful and not that cheap.
Happy polishing!!!
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