Everything Babs said
Lack of jobs and poor pay if you find one.
No help from the state if you find yourself in difficulties because you cant find a job.
It is very easy to get carried away with the pros and forget about the cons, but the lack of work and very poor pay if you are lucky enough to find one pretty much cancel out all the pros. The most successful ex-pat stories are from those with their own businesses, retirees and the already well heeled who can afford to live off rents and other private incomes. There arer also those that work overseas in Africa and the Middle East who have great jobs and use Cyprus as a base.
I've seen dozens of young people from the UK come over and be forced back because they really coudn't accept the low wages, or became depressed when they realised that work they could get was was relentless, boring and uncomfortable in the heat and the only accommodation they could afford was miles away from their holiday experiences that drew them here in the first place. The most worrying aspect are young couples that come over with children not really taking into consideration their educational and health needs. Cyprus is a great, friendly, sunny, pictureque, healthy and relatively cheap place to live (but not when your salary is so low - that suddenly things begin to look very expensive).
There are of course many successful young couples making a go of it in Cyprus, but I've noticed that those that do make it have some connection into the family and 'who-you-know' networks that Cyprus is famous for. For complete outsiders Cyprus can be a very unforgiving place with no support networks to help when things go wrong.
As you are young and it seems from what you've written fairly care-free, you have nothing to lose in giving it a go, but make sure you reserve enough finances for an escape route back to home in case things go belly up. Cyprus like most everywhere else is experiencing a recession - far fewer tourists and therefore far fewer jobs and those that there are are keenly competed for by a cheap labour force, some of whom are willing to work for a few hundred euros a month and pretty shoddy accommodation. Faced with that competition, finding even a remotely reasonably well paid job is going to be very tough.
Sorry to burst bubbles, but it's better to go into an adventure with your eyes wide open.