Salty,
I think she means 4 straight weeks of NOT seeing any problems. Things you may often see is: ick, velvet, fungus, parasites, droopsy, bloat etc. It isn't limited to those but IME those are some of the commonly encountered ones and the stress on the fish of moving to new quarters often brings out whatever the fish may secretly be harboring.
One note on the quarantine tank:
If possible, keep a quarantine tank cycled by keeping some cheap livebearers in there so the biological bacteria is well establised when you introduce the new fish. If you set a new tank up as a quarantine tank you will most likley get at least a mini cycle and more likley a full one which will last for about 5 weeks.
During this time the new fish , which is already stressed from new surroundings and new waterchemistry, is likely to experience ammonia burn , nitrite poisoning and shortage of oxygen to name a few.
As was mentioned above, a quarantine tank only NEEDS the following: Tank, water, heater, airpump , spongefilter and cover. Try to pull a mature (old) sponge filter from another tank. Also some artificial cover for the fish is a good idea - plastic plants, PVC pipe or flowerpots.