I had fun with Telstra a few years back. Not as bad as this, mind.
Somehow, during the course of my sleep, I managed to use all of my 1GB mobile data allottment, and then some, which would have resulted in a huge bill. So I upgraded the data pack to 2GB, which would have covered it. For some reason, my data usage went down, and all was well with the world.
Come the next month, I go to downgrade my data pack, and it errors out. Oh well, it's the weekend, I'll try Monday. (I don't know why that would have made a difference but whatever, didn't hurt to try.) So I try Monday and still no go.
The next day I toddle into the Telstra store and talk to a lovely woman there, who proceeds to spend an hour on the phone and computer trying to sort it out while I sit and play Angry Birds on my phone. In the end, she comes over and says "well they can't put you on the 1GB data pack again, so what we'll do is every month we'll credit you the difference and you can keep the extra data." Well, that's strange that nobody can seem to remove it. But cool! Free data! What's not to love?
Well, the next bill comes and there's no credit on it for the extra data.
So off I toddle to the Telstra store again and explain what had happened, and they tell me that they can't automate it, and I'll have to come in every month and get them to apply the credit for me. I think I did that for another month before I gave up because I couldn't be bothered (and didn't have time, I had started a new job that wasn't near the store) to keep going back there.
Also, when I signed up they put me in the Legacy system and I couldn't sign up for online account services as a result, so I had to get all my bills by post and had limited ways to check my usage during the month. When asked how I could go about being switched to the new system, they said that they couldn't force it and it would just happen one day. It eventually did happen, but why they put me in the old system in the first place is beyond me.
EDIT: also I've had fun with The Department Of Human Services (what we call Social Security here) where they managed to nuke my entire account. But that's another story.