Does a landlord have a right to continually collect rent (even though the late fee isnt included) and not say anything?

Late fees are only enforceable if they are lsited in a lease and described as additional rent. The fact that a landlord does not access a late fee does not mean he cannot seek it later. However he cannot base an eviction for non-payment soley on late fees but if you fall behind on rent and sues you for non-payment of rent he can tack on the back late fees to the total. You could argue that the late fees were waived but unless they go back a real long period of time (9 months to a year) the Judge will in all likelihood grant them. Most courts in New york frown on a landlord who refuses rent when the late fee is not included so many landlord will accept rent anyway but still keep track of the late fees in case they have to evict. They also sometimes will deny a renewal on the basis of late payments or non-payment of late fees.

I don't understand.   If you are late, the landlord can choose to simply take your rent and not charge you a late fee.  If he or she does that, and the late fee is stated in your lease, then arguably he or she has waived that provision for that time.  If it occurs more often, then arguably he or she has waived that provision permanently for you based on the pattern of your payments.

Hope this helps.