Will Laser Resurfacing Cause Long Term Damage?

I am not aware of long term negative consequences other than a slight tendency to be more sun-sensitive, but everyone who has had a CO2 laser should be using sunscreen to continue protecting the results that were obtained by the laser. There have been cases of delayed lightening of skin color, noted as much as one year after surgery.

Older CO2 laser skin resurfacing effectively removed wrinkles but also thinned the skin. Because of the skin thinning, the post-resurfaced skin was more susceptible to sun injury.
Newer fractional laser skin resurfacing actually builds new collagen in the skin and thickens the skin. There should be no long term damage that could increase skin sensitivity to sun or other potentially damaging factors.
There is both non-ablative (Starlux 1540 and 1440, Fraxel, and others) and ablative (Starlux 2940, Fraxel Repair, Active FX and Deep FX, and Profractional) fractional laser skin resurfacing lasers.
Non-ablative plumps the skin, ablative vaporizes damaged skin and plumps the skin.
See before and after pictures of Fractional laser skin resurfacing.