What kind of problem do you expect? Shouldn't be any if you behave.... I crossed the border yesterday from Greece no problems. I will be adding to my post probably tomorrow when I get time to complete what I've done tonight maybe as I was knackered yesterday after 12 hours in the saddle.
The biggest problem you'll have is the Russian border with Georgia. Theyre not friends so the border is closed currently. The way round it is to get a ferry from Turkey to Russia - pretty easy, but defeats the aim of a total Black Sea circumnavigation in my book.
L's right, currently it's not possible to cross the Georgian / Russian border. You'd need to get the Trabzon / Sochi ferry, which apparently is a crane on / crane off affair. Things might have changed by next year though, so it's worth keeping an eye on the situation.