Just as an aside, there's a new formula of Autoglym Super Resin polish which seems residue free. Worth trying - on Amazon. Autoglym is the Marks & Sparks of polishes, Megs and Zymol are a bit more Bond Street. Having said that, Autoglym is really good stuff - the new formula particularly.
Steve.... As to your small circular marks. It's very hard to say what they might be - it certainly sounds like water marks. Just go really easy on anything you do - you won't do damage with a clay bar, but cutting polishes can be difficult.