Stuff to look out for:

Bike is worn out: pointy cogs, crunchy bearings, chalupa wheels, stuck seat post or stem
Bike is of a brand you can't determine
Bike was made in France or England (but those brands ok once you're in the Japan/Taiwan import era)
Bike has steel wheels

Stuff to do:
Clean & grease everything
Replace tires (Panaracer Pasela, Michelin World Tour, Kendas and some others still available in 27")
Replace brake pads
Replace cables ($10 Bell brand kit from Wal-Mart)
Replace chain (7/8-speed chain with a quick link works fine on 5/6-speed freewheels)