Hi Ken!!
I have bought/rented out and sold a place in Buenos Aires and also currently own some property in Cape Town, South Africa. I don't know anything about the Romanian market or Eastern Europe. From my experience investing oversees can be done if you have great team in place. The guy I worked with in Buenos Aires was awesome but it would have been a nightmare without him filing my taxes for me, keeping up with all the Argentine real estate laws, fixing things that broke down, etc. But that being said there's alot of things about investing oversees that can be a pain or certain quirks in the laws that you need to be sure to know. For example in South Africa the law requires that when you sell a property the money has to first be deposited in a South African bank. I can't have the buyer wire the money directly to me in the states. But the South African bank will not accept the money unless you show proof of where you first wired money into the country to buy the place. This law was not in place when I first bought there ......it changed... some kind of anit-money laundering law they enacted. Luckily I keep everything so wasn't a problem but if I had thrown away those receipts I would have been in trouble. Also when I get income from my rentals deposited to my South African bank account I have to send the bank the receipts to show where the money is coming from otherwise they reject the money.
Another issue that can work for you or against you is the currency exchange so that needs to be factored in. Plus investing oversees I have not found good lending situations like what we have here in the states. In South Africa as a foreigner you can get up to a 50% loan and the interest rates are high....around 10%plus and the rates fluctuate. The interest rates in general are higher there cause you can still put money in a savings account and earn 5% unlike here.
Also if you're married or in a partnership etc. the laws could be different over there in regards to that, that you may want to look into. When I signed the paperwork in South Africa the bank I was getting a mortgage with made me sign a piece of paper stating that I would let them know if I ever got married. I asked them why it mattered if I was married or not since I'm buying the property as a single person. They told me because the laws are that once I'm married the other person is entitled to what I have and that if my spouse for example had a gambling problem I'm responsible for that debt too unless I had in place in South Africa what is equal to a prenup over there.
So my point is just learn everything you can about the laws as there can be quirks that you might not know about. But that being said some of these oversees markets are growing quickly and could have good appreciation. I've had friends that made alot of money investing oversees but just be careful.