None.  Assuming you are buying in the Republic of Cyprus – which is the only part of the island where you can legally buy property – you can buy anything you like.  In Cyprus we sell freehold, and Rimentalia guarantees you your title deeds as soon as possible after the purchase is successfully concluded.
Cyprus is happy to be in Europe, and European regulations apply.

What is the voltage of the power supply in Cyprus?

240v AC – just like in the UK.  All of your electrical appliances will work just fine here and – in all probability – you will be able to get them serviced and repaired in Cyprus too.  Moulinex, Sharp, Panasonic, Hotpoint and Hoover, to name a few, are household names over here too.
And we drive on the same side of the road too!

How can I communicate with home?

We hope Cyprus will be your home!
But Cyprus happens also to be a major telecommunications hub for the Middle East with broadband internet connectivity and cheap, good quality telephony.  Failing all else there is a competent postal system for Christmas cards but personally we generally prefer to use digital!

How do I travel?

Within Cyprus we have a good network of quality roads including a motorway system between the major cities.  (They have two lanes rather than three and the speed limit is 100 kph) Bus travel exists but is not too frequently used,
Taxis that work communally rather than for individuals are common and economical; they are called “grammez”.  Although they only run at fixed times and you will need to book a seat by phone, they will pick you up from your door and drop you off wherever you want to be Cyprus-wide.
You can bring your car with you from the UK – but car air-conditioning is a good idea for the summer months.
Outside Cyprus we have two international airports and a seaport at Limassol for cruises around the Mediterranean and cargo (if you want to bring a container from the UK.)

How is the crime situation in Cyprus?

Generally very good – you can walk the streets without anxiety and you do not need to live in fear for your children.  Get some statistics – the hard facts – here http://www.nationmaster.com/country/cy/Crime

Will I need to learn another language?

 It’s a good idea to lean a little basic Greek – yes, no, please, thank you, hello and goodbye, but you will not NEED to do so. 
English is spoken almost everywhere and government offices and civil servants are required to speak some degree of the English language.

What do I do for healthcare?

As a citizen of Europe, you can cover your healthcare costs with the appropriate form.  The E111 covers all tourists and if you ask at the local (Cyprus) hospital or in the UK you can arrange the appropriate cover for Cyprus without extra expense to you.
Get full details here from a Cyprus Government Website