I noticed some operators check Pinball Map frequently and pay close attention to problems on the machines reported onto there. Whoever operates the machines at the Lake Forest and Aliso Viejo Ice Palaces, for instance, is quite prompt with them (or, if the problem is something that can't be easily fixed, will shut them down or swap them with another machine). It's pretty neat.
But yeah, that's about the extent that an operator can do. Otherwise, if no one directly contacts the operator (which can't always be done), they won't ever know about it.
Since getting ahold of an operator is often way harder than I would've expected, I keep some Post-It Notes in my car, and if there's a problem with a machine and I don't know of a way to contact the operator, I write down the problem and put it on the machine. (Asking the people who work at the establishment is usually useless--I've never had a case where they know who the operator is, or they refuse to tell me because they think it's a privacy violation or something.) My Post-It Note system worked with the Avatar (and later Shrek) at Granada Hills Bowl, for instance. It's backfired on some other cases though: I reported a broken Terminator 2 at Ray's Original Pizza at UC Irvine, and that caused the operator to remove it without a replacement. (Apparently, it was sold off.) Post-It Notes are removed from machines at Family Amusement Corporation without them being fixed either.