I don't really like to say it, but I will be blunt: contractor ground services suck. Hopelessly. Period.
To be almost brutally honest, if FFPs didn't exist (and further if premium classes and extra charges, e.g. exit rows, also didn't exist), contractor ground services actually do a pretty good job.
In one way, since most of NZ's services from SYD are merely Trans-Tasman, it's not an overly complicated matter. The FFP matter might be the most difficult part of the job, as also with Seats to Suit, but if NZ has a system about it then I'm sure even a child could do check-in, too. Besides, even if the FFP part is slightly stuffed up, I don't think it's a major failing.
In my experience, contracted services like Toll Dnata and Menzies take no prisoners when it comes to luggage. MH have been handled by a contracted service in BNE I for ages, and my mum has even been pinged for being 1 kg overweight on checked baggage. Yes, you can't break the rules as a passenger, and they are doing a job, but just saying that for those who may pack quite a bit with them.
To be fair, even check-in by another airline's staff is not necessarily good either, though my negative experiences with airline staff doing check-in for another airline are all overseas, not in Australia.