I put a link on facebook. Regular link the website. When people went there to check it out the shopping cart was shared among those people. So if one went to the page and added a product and then the next went to add a product then he would se both products. Even worse when one logged in, it was also logged in for other people to see.
I tried to test it. Took a brand new browser, deleted history and cookies. Went normally to the website and no problem. Deleted history and cookies and went through FB and now there was something already in the cart.
How is this possible? I was really in chock and had to remove the links!
I was in chock as well. Like totally in chock. I just wrote www.(nameofmysite).dk and people went there to have a look and reported the problem.
I might have resolved the problem. My hosting provider added a new feature that should increase my cache a lot but appartently there were some problems with it that might have caused this big issue. After disabling it I have not been able to reproduce the problem.
It sounds like your hosting provider implemented a server-based full page caching solution for you. These rarely work 'out of the box' since you obviously do not want to cache pages that contain user data and the like; they need to be a little bit smarter - which is where a software (extension) solution can help out.
If you're still after an FPC (full page cache) solution - Magento Enterprise has one built in; if you're running community edition there are many different FPC solutions available - some free, and some paid for. One's I have used myself in the past are Nitrogento and Lesti FPC - I have no affiliation with either and you should always evaluate which solution works best for you, and where possible - always test in a dev environment. When testing things like full page cache its always handy to test in multiple browsers too (to simulate multiple users.)
Hope this helps - and good luck.