The answer: yes and no. There are two notable locations where the world is broken up, one worse than the other. First is the gap between the Shire and Ered Luin. The long range plan is to have land between those two locations at some point but I have a feeling it's a little low on the priority list. I'm not one that cries out about my immersion being broken. If I were, it was broken a long time ago. This is a game, there are limits to how closely it can follow the source material as a different medium (just like the movies). However, certain aspects of the game world natrually lend themselves to the IP, one being a large and seemeless world.
The real reason this question comes up is because of the Mines of Moria expansion. Moria is one large dungeon. One large instance. Now, the tech behind it is more like an overland zone than an instance, but it is nonetheless seperated from the rest of Middle-Earth by a loading screen. Does this seperation hinder the continuity of the world? I'd say not so much as the Ered Luin/Shire break. Those are both overland zones which shouldn't need a loading screen between them. Moria on the other hand is almost like a seperate world in and of itself. The books described Moria with a whole new character and presence than it did the rest of the world. And in Tolkien, the land was as much a character as any of the Hobbits, Dwarves, Elves or Men. Some might even argue Middle-Earth was better characterized than Sauron himself, but that's a debate for another day.
Honestly, I port around Middle-Earth so much that there's as much of a discontinuity in the Shadows of Angmar content as there is between there and Moria. Being the Tolkien junkie that I am part of me really wants to stop porting around all over and ride to where I neeed to go, but dang it I just get bored. Not that I don't enjoy seeing the scenery of this game. It's beautiful even if you've seen the same thing over and over again. I want to play the game most of the time, not take a virtual tour of Middle-Earth. There's a time and a place for the latter, don't get me wrong, but the game mechanics have almost negated the need for a continuous world. Almost. I want to know that it's there if I ever chose to experience it. I want to know it's there because it's the right way to build Middle-Earth. Both game mechanics goals and world representation goals are fulfilled so far, for the most part.
To me, there isn't a big jarring jump between Moria and Shadows of Angmar any more than there should be. Moria is a different world in a sense but it still retains it's Middle-Earthiness. I've heard talk about World of Warcraft's expansion zones not needing any relation to the rest of Azeroth because of the discontinous world. I'm not here to critique that type of expansion - it works for WoW, clearly, but I appreciate the interconnectedness of Turbine's Middle-Earth and venture to say I'd enjoy this type of world building better.