It would help to know what kind of brake you're actually using, old World Sport is either side-pull caliper or centerpull caliper. There is no "side-pull cantilever" unless you count V-brakes which your bike certainly does not have.
Most brake/shifting problems are cable related. This will help:
http://sheldonbrown.com/cables.html
Also, some of the brakes used on the 80s World Sports are absolute garbage and will never provide adequate stopping power no matter what you do. My parents have a pair of '84 World Sports (which they never ride) with some terribly flexible Dia-Compe brakes. But either way you should still be able to get them to work smoothly.