Relevant Information:
I have a 2002 Trek 5200 (history unknown). I got the bike in what I would consider very nice condition. It does not seem to have been abused and the frame appears intact and solid. There are no scratches or apparent disturbances to the rear dropouts. When I received the bike I had the rear wheel trued. The bike has what I would consider close to vertical dropouts.

Problem:
When (any) rear wheel is installed and positioned securely up against the dropouts the wheel points about 3-4mm towards the drive side chain-stay. The wheel is not parallel to the frame. The tire clears the chainstay but it's a little too close for comfort and I'm prevented from using anything larger than a 25mm tire. When I position the left side of the axle up against the dropout the wheel will be centered. But then, when I pull the right side of the axle up against the dropout (appox 2mm of play) the wheel is off centered.

Question:
Is it dangerous or ill-advised to ride the bike with one side of the axle not securely up against the dropout? I can tighten the QR just fine. Is it possible to purchase a shim that would fit inside the dropout? Is filing down one of the dropouts by approximately 1mm a possible solution or will I been degrading the integrity of the dropout? I'm sort of leaning towards the filing solution.

Let me know if you need any more info or if I may have not described something clearly.

TMT