The attic of my house has serious ventilation issue and the sheathing becomes rotten. The roofing contractor suggests me to replace the rotten sheathing and install some ridge vent. His plan will also keep two old vents on the ridge. I once heard that the co-existence of different types of vents will cause the air flow formed among these different vents instead of a smooth flow from soft vents to ridge vents. Is that correct? How to insure the ventilation plan proposed by contractor is correct?
You should read up on some of the roof ventilation articles at Building Science -- they provide a lot of resources and actual studies.
While "adding more ventilation at the peak" is an "easy" thing for a contractor to fix, the first thing that your contractor should be doing if you have mold issues is to make sure the soffit ventilation is working adequately... or that you even have soffit ventilation. The way that most roof structures get ventilated is that air enters through the soffit and exits through the peak due to convection on the roof. The reason that mold is building up is because either air isn't exhausting or air isn't moving enough through all of your bays to dry it up. Just throwing another couple vents up won't necessarily solve this problem.
Where you run into problems is where you have vents of the same type on two different sides of the roof. Because of this, ridge vents aren't really a great solution -- call me a traditionalist, but my preferred attic ventilation solution is turbine or turtle vents on one side of your roof at the manufacturer's recommended distance from the peak, and more-than-adequate soffit ventilation.
Soffit ventilation often gets interrupted because it was installed inadequately in the first place or blown-in or even batt insulation gets shoved into a place where it blocks the flow of air in. You should have baffles in place in any of your attic bays (between the rafters) that have soffit ventilation. My personal favorite as far as operation and installation are Berger Accuvents. (Note: Link is to PDF.) I also prefer continuous soffit vents. If you don't have soffits, you should look into a product that you can apply to a roof without a soffit, such as a vented edge cap.
It would really help to know where you are, because attic ventilation needs are different in different climates. If you live in a climate that experiences winter weather a significant part of the year, you'll want to make sure that your attic ventilation remains clear.
If you install ridge vents but leave the old can vents, you have negatively effected the efficiency of the new ridge vent.
Intake (usually under the soffitt) needs to be equalized with the exhaust and you need to make sure there is a clear passageway for the intake air. Baffles are often used to ensure no blockage from insulation.
If you have excessive moisture, you should also check to make sure bathroom vent fans are being discharged above the roof and not in the attic or under the soffitt.
And last: find a new roofing contractor, as the one you have does not know what he is doing.