Your lease requires you to cooperate with the landlord in making the tenant ready and available for the next tenant. Thus, you are obligated to cooperate in making repairs to the floors, whether or not there is immediate mold danger. Further, in a situation like this, delay in repair is likely to make the situation worse.
Ordinarily, tenants are not responsible for damage due to defects in basic plumbing, such as toilet fixtures, pipes that run through walls and ceilings, etc. But your "kitchen sprayer" might be a different story. Your best argument would be that the super took charge of hooking it up, and that his installation called the problem. But the landlord may contest this argument, and attempt to hold you responsible. I have no idea what the actual facts may be---but one thing is sure---it will cost more in legal fees for you to fight this issue rather than to settle with the landlord. Your best bet is to work out a compromise---you let the landlord make the repairs over the next couple of weeks and the landlord gives you back your security deposit---or alternatively, you split the costs of repair with the landlord. A negotiated solution is the best---but in truth, the landlord has the upper hand legally on these issues.