Increased congestion. Many of the Zicam nasal sprays contain nasal decongestants, similar to the afrin brand of nasal sprays. Topical nasal decongestant sprays are safe if used for a short period of time. If used for more than a few days, however, they can cause rebound congestion, which can become more severe than the original reason for using the spray. Never use for more than 3 days straight.
Permanent damage. Zicam zinc based nose sprays have been implicated in a number of reports of permanent or semi-permanent loss of smell. I would just stay away from it.