Looks like you have two options:

Option 1:

1. Address any complaints that could be both legit and your responsibility. For example, A/C could still break down after tuneup, so you should check it, mold can appear, but neighbor stuff not your responsibility (unless they are also your tenants).

2. Ignore other complaints

3. Periodically re-offer "happy clause"

4. Collect rent

Option 2:

Begin eviction for late payment of rent, in spite of the expense and difficulty.

I do not understand the title of the post. Sounds like they are paying, but just paying late and whining a lot. Here's what I do:

#1 - Late fees for late payers. I do $5 a day after the 1st which is the day rent is due. There is no grace period. Check with your attorney as far as what's legal and enforceable in your state. In MO we have no statutory cap on late fees and can begin charging the day after rent is due, but my local judge tops out at $150. His thought is 30 days you out to have them evicted by then anyway...or pretty close. Also, establish a "drop dead" date that you file eviction. Mine is day 7, so if I have no rent and no reasonable plan for them to get caught up, I send the lease to my attorney on the morning of the 8th. Having that decision made up front removes much of the stress of deciding what to do. It's like a flow chart and you just go with the flow. Hiring an attorney costs more than DIY, but the cost to me is worth the aggravation, time lost appearing in court, and possibly doing something wrong that allows the tenant to delay the eviction.

#2 - All repair REQUESTS must be submitted in writing. No, a random text saying "AC's broke" doesn't cut it. I want to know the date the issue was first noticed and what is the specific problem including any common sense approaches they've taken to address the issue: "Air conditioning fan hasn't been coming on since Friday July 4th. We tried resetting the breakers and checking the thermostat battery. Still not working."

Emergency requests are responded to immediately within 24 hours. Non-emergency get put on a list to be addressed within 30 days (usually same week if not very busy).

Warning: excessive, frivolous complaints are often a sign that the tenant is about to stop paying rent and use this as an excuse for withholding rent. Don't fall for that tactic. Bare minimum, the day rent is late you stop by and check out the issues. If bogus, proceed with eviction immediately because you know now they are broke and you will end up evicting anyway. The only question is how quickly you get your unit back.

Cost and hassle of eviction should not be a factor when that has been confirmed as the appropriate action. You knew those going into this biz--or should have. Again, you will either pay those costs now or later. Allowing deadbeat tenants to remain only increases your losses.

When does their current lease expire?

Have you ever served them with a 14 day notice to quit for non-payment?

Have they given you written notice about any of the unit's alleged defects?

Have they ever withheld rent due to alleged defects?

Does your lease contain a late rent penalty?

Do you own the entire building or is this a condo?

As Gwen suggested check out any & all of their complaints, address the legitimate ones & ignore the rest. Any time the rent is late issue them a 14 day notice to quit. You can do this yourself just make sure you use the form for term leases not MTM agreements. Since they have a lease MA law allows them to cure late rent through out the entire lease term provided they pay rent & any associated charges by the court answer date.

Unfortunately unless they do not pay the rent, do not commit any illegal actions, are willing to accept a cash for keys offer or otherwise voluntarily leave, you are stuck with them for the entire term of the lease.

If these were my tenants I would make sure to properly notify them at least 30 days prior to the end of the lease term that I was not going to renew or extent their lease. If I thought that they would not actually leave, along with the non renewal notice, I would offer a new MTM agreement for substantially more money.

Only thing I would add ... my LATE FEE was contested by a tenant in court and had to be removed from the lease per a judges order. MA is tenant friendly.

Tyran, would you mind sharing your late fee amount and the court which said you had to remove it?

According to MA law a LL may charge a reasonable late fee provided it's written into the rental agreement & does not kick in until the rent is 30 days late. My local district court & housing court judges have always allowed my late fees.

Face the music, go and do battle. Maybe you will spend some money. But these people will cost you your health and sanity if you let them.

Non payment of rent => that's your leverage. Use it. Get them to court. (I know nothing about the process in your state - hope it won't be as bad as you say).

My PM agreed to a rent reduction to end the constant harassment in a similar case I had. That involved "mold" and several lab tests. The tenants had some DIY test kit and my PM hired a lab which sent its own personnel...

Well, it was all b.s. and due to tenant not reporting some leak.