The "people" vs. "things" distinction strikes me as unhelpful. It kind of works for the specific example given of "boring" vs. "bored" (actually, it doesn't work all that well for "boring", as has been pointed out) but really it is much simpler to consider the syntax of the related verb:
Participles ending in -ing almost always "modify" something that could be the subject of the corresponding active verb. "School is boring" is approximately equal to "School bores [people]".
Participles ending in -ed or -en usually "modify" something that could be the object of the corresponding active verb. "I am bored (by something)" is approximately equal to "[Something] bores me." (This holds if the participle is derived from a transitive verb—the -ed/-en participles of intransitive verbs sometimes can be used with a non-passive voice meaning.*)
So, the question is, do you want to talk about "repeating complaints" (= "complaints that were repeating" = "complaints that repeated") or "repeated complaints (="complaints that were repeated (by someone))?
Either one is technically grammatical. But usually, we think of complaints as things that are repeated by people, rather than things that repeat on their own. So "repeated complaints" is more common than "repeating complaints".
Here is an example of the latter wording:
However, other than the ever repeating complaints that certain predators, for example whales, seals, and dogfish sharks, were responsible for declines in fisheries, ecological studies were not thought to be required to provide the advice needed for managing fisheries.
(Scaling Fisheries: The Science of Measuring the Effects of Fishing, 1855-1955, by Tim D. Smith, p. 332)
One particular reason why the phrase "repeating complaints" may be avoided for the most part is that the -ing form of a verb can be used in a number of other ways, which may cause ambiguity. In the example sentence from the question, replacing "repeated" with "repeating" would make possible the incorrect intepretation that the landlord was making the complaints:
After repeating complaints, the landlord...
(could mean "After he took the action of repeating complaints, the landlord...")
*: such as fallen