I work in a impartial mobile phone shop, so we sell all networks and tend to see all the problems as well as all the positive customer service experiences.
Since I started the job 2 years ago three has always been consistently the worst when it comes to customer service and outright lying...
We have a few demo iphones in the shop and sometimes we will get cold calling from three sales call centres, one of my colleagues decided to have a bit of a play with them once and pretended to be a customer thinking of upgrading, he asked them a few questions to see if they would be honest or lie to him. They lied about all their call centres being in England, then he purposefully asked for a phone that he knew had had a hell of a lot of faults.
Even the manufacturer had recalled them due to software issues! He asked if there was any problems with the model of phone stating he had read about the faults in a magazine. The guy on the other end of the phone blatantly said it was a great phone and one of the most reliable if not the best phone to choose and that they weren't aware of any faults.
This isn't a blanket statement saying three lie to you, it could have been a third party selling three phones or it could have just been a sales rep not completely up to scratch on his phones. But seriously...I have always had the impression of the poorest customer service from three since i started the job. Its what my colleagues told me when i first started and its what iv experienced after sitting on the phone for a good hour trying to resolve an account issue for a customer. Sometimes its something as simple as a number port and the three customer service rep on the phone asks to speak to the customer to confirm DPA and before you know it he's trying to push insurance, if they want mobile broadband or some other sales junk.
At least the other networks only tend to get pushy with sales if you called their upgrades department, generally if you call for a number port thats what they'll sort for you, quickly with little hassle and end the call with "Is there anything else we can help you with?"
Other problems with the three network that we see daily, are customer putting contract sims from three in sim free unblocked handsets and then receiving texts saying "Your handset is not a three handset and has been blocked". No other network does this.. and where as this isn't a customer care problem it is a problem that gives angry customers a reason to jump networks.
I have twice seen o2 wave bills over 200 quid for customers as a one off customer care acts of kindness, because the customer has been genuinely unable to afford to pay their bill. One occasion it had been their son who had run the bill up browsing the net on the phone and the other occasion it was a pensioner who's grand daughter had done similar. I've never really seen this happen with any other network.
Terms of how id personally rate networks:
T-Mobile (their welsh disconnections department is lovely)
Vodafone (ton of messing about sometimes with phones not connecting or number porting, but maybe thats just because we aren't vodafone direct)