The Doctor is probably somewhere around Dr. Strange level. I'd put him slightly higher, but then again I'm a Doctor fanboy.
Within the Authority's mythos, the Earth has always had "a Doctor". He has been reincarnated hundreds of times, and has access to the shared knowledge of every previous Doctor (he can communicate with them directly via some strange telepathic/spiritual realm)
Doc has quite a few powers...His main power is the ability to manipulate matter through sheer magical force. He's turned battalions of random bad dudes into trees, ravens, etc. (usually something environmentally based...as the "Shaman of Earth" he is very ecologically conscious). He has also transported beings to different dimensions and has some limited time travel abilities (don't know the exact extent of them). Any being without magical shiedling would be vulnerable to these kinds of attacks.
He also has the ability to communicate with others telepathically, but does not appear to be at the same level of telepathy as, say, Xavier, Manhunter, or any of the other powerful comic telepaths. He hasn't attacked anyone telepathically, but once broke the telepathic hold on thousands of people by a powerful evil telepath. His last ability is telekinesis...rather powerful in this department...he once held most of Italy in place while the world turned on its access, flooding most of Italy.
Since he is Earth's Shaman, his powers are enhanced when dealing with Earth-based things. Thus, he could hold Italy (part of Earth), but can't telekinetically lift objects that would have the same mass (though he can lift himself, giving him the power of flight).
That's him in a nutshell...the current Doctor (picture in my sig below) was formerly a drug addict (couldn't deal with his immense powers) but has since reformed and is an uber-powerful shaman.
-DM