This is a reply to the whole thread; hopefully it might be helpful to anyone who is still experiencing problems. This is a round-up of the tips I have, some of which have already been posted ITT.
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1. Please make sure you are signed in with your iCloud account on both your mobile device as well as on the computer you are trying to view your iCloud tabs with.
2. Please make sure you have not set either your mobile device's Safari browser, or the computer's browser to Privacy mode.
3. Please make sure you have enabled Safari to be used on iCloud. It looks like this on a computer:
4. If you are connected over Wi-Fi and/or a LAN on any of the devices, please try and make sure there aren't any settings on the network blocking this services. I noticed, for instance, that having UPnP switched off blocked the services for Notification Centre in OS X 10.8.x.
5. Please try and make sure your computer is running a version of OS X that supports iCloud tabs.
6. Please check if it would help to set OS X to automatically set the date and time (and that your Time Zone is correct, too).
Allowing OS X so automatically set the date and time has been proven to help many people with issues regarding another service, namely iMessages. So, this might not have any impact in regards to this matter.
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You might also be wise in rebooting your system after making changes to settings. It might not hlep at all, but it can sure help save a lot of grief and anger if successful. This will especially apply to people who enable the Set date and time automatically option.