Lots of threads on this, so yes, it is a common problem for some. Might be useful to keep a set out next to the computer so your brain gets used to both views. I've been known to have as many as 6 or 7 sets out at a time, 2 at the moment. You could do a search for "2D vs. 3D". Here's maybe 5 or 10 threads worth reading:
http://www.chess.com/forum/search?keyword=2D+vs.+3D
It really depends on the player. Some people have a hard time going back and forth between 2d screens/images and a 3d set. I've heard of people who get no benefit doing tactics puzzles from a book, because it doesn't help them spot the same patterns on a 3d board, so they have to set up every position to do the puzzles.
Personally, I don't have that problem. I can go back and forth fine.
What I have found is that with a slightly smaller 3d board than the tournament normal size, I can take in the entire board at once better. I once saw a post online from a master who said the same thing - he was stuck around 2000 rating until he switched from the normal 2.25 inch square roll-up board to one with only 2 inch squares, and then his rating suddenly shot up 200 points to master level. I have a rollup mat with 2 inch squares for this reason, though most of the tournies where I live now supply the equipment, so I don't get to use it as much as I used to.
I haven't actually played in real life since I started playing on here...but I often think of asking my friend who I used to play with to play sometime, and always imagine I'd struggle with the transition and not be able to see things the same.
It seems different to me at first but it goes away after a while. Forgetting to hit the clock can happen sometimes.
I'm always paranoid of this when I'm going to play over the board because I play so much on the internet, however, never been a problem. I always am a lot better at reading a real board than a computer screen. All that to say, this is an issue with me when I play Go so anytime I play on a server, I have to keep a real board in front of me and follow along because I'll be all mixed up when I go to play over the board if I haven't done it in a while.
I practice with an Excalibur Grandmaster chess computer (almost full size) prior to playing over the board. Previously I found the transition from 2D to 3D very difficult.
It is different but i always prefer face to face chess. To me the difference is the game seems more intense when it is face to face. When you lose (or win) online it just doesn't have the impact as face to face. Also a big difference is here (or nearly any other online site) you know the rating of your opponent so you basically know how hard of an opponent you face. In offline play unless you have played the player before you have no idea how strong his play is (unless its a rated event of course).
Most of the time of i am playing a friend of mine and a stranger walks up and requests to play the winner they tend to be very weak players. This is even more likely if they brag about what a strong player they are. Really good players are usually very modest and often downplay their strength.
Of course online play has its advantages. You never have trouble getting a game no matter the time of day/night. You don't have to drive anywhere just walk over to your computer. You also can chose the time control and also (to a large extent) the strength of your opponent.
As far as adjusting to the visual aspects of it that has never bothered me.
A few years ago, after quite a bit of playing chess exclusively online at Chess.com, I found myself at a coffee house locally, where some chess players had met on the weekend to play each other.
I asked one of them, who was sitting by if he wanted to play. He rolls out a green and white tournament style board. And it is slightly creased in places and doesn't lie perfectly flat. Then he starts acting kind of crazy (he looked remarkably similar to the pictures of Jack Black, in this OP, at about 20% of the transformation from the first pic shown to the 2nd one shown) and started acting kind of unstable and kind of mumbling to himself and nonsense. I'm thinking, if I humor him maybe he won't get violent.
As we played, I found it difficult to adjust my perceptions to the large format board and pieces, and blundered egregiously, every early in the game in ways that weren't reflective of how I was playing online at the time. Even though he was probably trying to psyche me out (he didn't seem to act as crazy with the crowd he showed up with, I noticed at a distant table as I finished my lunch), I felt my playing suffered more from the switch to the different board and playing with real pieces than from anything else.
Is that a common problem for chess players?