We've run into many problems trying to find an apartment here. Often we find the perfect one, only ot find out that the landlord keeps saying "no problem" and the building says "no way".
At many places the doorman/concierage will turn a blind eye to the pets coming in the building, but if neighbors complain it can become messy. I would just make sure to befriend your neighbors and make sure they come to you instead of complaining first. Most often it can be worked out.