Tire size / rear dropout incompatibility? Recently my commuter bike (cannondale quick 5) was stolen, so I decided to get an old road bike off of craigslist - a '91 specialized sirrus triple.  The guy I bought it from had bought it new, used it for about a decade, then hung it up in his garage until this past month. I took it in to REI for a tune-up and some new tires and asked if they could put on tires with a bit more traction, knowing that I'm accustomed to my commuter bike and probably wouldn't do too well with slick tires.

When they put on the new tires (I'm not talking knobby mountain bike, just a little bit of tread - Michelin City tires) they had me sign off that the change in tire size meant the rear wheel would have to not be completely in the dropout - currently it's about halfway in the dropouts and has scant 1/8" clearance from the rear brake assembly; if it was all the way in the dropout it would have no clearance whatsoever.

Is this (the rear wheel not being completely in the dropout) ridiculously unsafe?  I've never had to deal with this before, but it seems like this would be ridiculously unsafe.
Yes, it is unsafe. You should find a set of tires that will allow you to seat the wheel properly into the drop out.