Below is a list of common, expected issues that may be created for you by your new landlord, as he tries to figure out ways to harass you into leaving your apartment. The left column indicates a generalized issue, and the right side, a suggested approach for you to take in each case.

Remember to record every experience in a jointly updated spreadsheet.

Problem Solution
Unwarranted contact …If a call, you can tell the landlord that you do not wish to speak with him. Alternatively, you can record the call, and let him continue to harass you while you effortlessly gather evidence.
Lease not renewed …If your apartment is rent-regulated, the landlord must send you a lease renewal, 3-5 months before the end of your current lease. Once you have signed and  returned it, the landlord has a legal responsibility to send you back a signed copy of it within 30 days. Demand your lease.
“Notice to Cure” Hire a landlord/tenant lawyer. If as a coalition we manage to get a specific attorney on retainer, that step won’t be necessary, saving you a lot of money. Send a copy of the notice to the lawyer and have him/her respond to the landlord directly. If, as usual, there is no merit to the notice, the process will likely stop then
Eviction notice (See the bit about you or the coalition getting an attorney on retainer above.) Send a copy of the eviction notice to the lawyer and have him/her respond to the landlord directly. As above, the process will likely stop once this has been done. If there is any merit to the notice, then you can submit and leave your apartment, or know that your personal cost to retain your own or the coalition lawyer will go up, as you defend your rights in further legal proceedings.
No heat/No hot water Call 311, or download the 311 app and report it immediately. The landlord must supply hot water to the apartment 365 days a year. Heat must be supplied under varying conditions
Excess Construction Noise/Dirt Make sure that the construction company has had the unit(s) undergoing demolition tested for lead dust, and demand access to the results.

Call 311, download the 311 app and report it. If there are children living in the building, make sure that you include that in your report. An inspector will be sent, but usually not for a few days. Demand that the construction crew keep dust levels to a minimum by working carefully and mopping repeatedly. They should mop at the very end of each workday as well. If they do not, then insist to your super that a final daily mopping be done.

LEAD DUST There’s a page specifically for this problem here.
Divide and Conquer Unite and Overcome. Really get to know your neighbors better. Form individual building tenant associations, and meet at least monthly to discuss matters in the building. Select a person or two to represent your building in a wider coalition, if numerous buildings are being mishandled by the same owner. Hold community-based events, and offer to help out if a neighbor needs assistance. Invite your elected representatives to meetings and gatherings. Establish connections with local (and less local) media, and talk with them if your landlord does something unethical, underhanded, illegal and possibly newsworthy. Create a digital communications network for your coalition, and a public website for it.