They just wrote to me complaining of getting sick due to possible mold - while they cannot point to visible signs of mold, they claim they smell mildew and mold like odors which are making them sick.

And that may still not get it all...I had to re-texture all the drywall one time due to odors.

There was writing in the shower wall (played tic tac toe), oven was bad, fridge dirty, pet hair on most of the baseboards and an odor.

The main problem was dog odor.

Evidence of water leaks, fire, smoke, foul odors, sounds indicating the possibility of an injured person or animal and other similar evidence of an emergency shall all be sufficient grounds for Landlord and Landlord’s agents to enter Premises and Property for this purpose."

Quote from @Chris Geer: When someone smokes outside, the odor clings to them and they bring it indoors with them.

Quote from @Craig Martens: Unfortunately, you can't restrict him from smoking it outside and he is going to drag the odor in with him.

She'll grumble but she won't move. 

What odor(s) do you smell.

Is this the first you're hearing about the odors and noise?