I think the point is less 'IT'S UNREALISTIC' and more that it breaks suspension of disbelief because more people are knowlegable about MMOs than they are about quantum physics. And more to the point, have spent enough time in MMOs to understand how and why they do as they do, which is why it's more egregious.
How is what UG gave as examples breaking your suspension of disbelief though? The way the story sets it up, the copies and tool are sent to individual user's computers so that they might make their own characters/worlds. It also mentions several companies do so as well.
Ignoring the potential even for advances in server, computing and otherwise advanced technologies (we're talking about a show that involves losing complete consciousness of your physical body to participate in a world that has shown that you can feel pain), I don't find it unreasonable to think people could be using their home computers as points of entry for their own worlds. Others could potentially connect to an individuals computer through IP and participate with their server created world through a similar client interface. We have been doing that very thing for years.
For his question on how to share large amounts of data between servers, I frankly cannot answer. Perhaps something in the original programming does it and connects to other individual's servers automatically. I simply don't know but it doesn't catch me as something that is out of the realm of possibility.
On the last point, how can someone make an entire full fledged MMO by downloading a single tool? Again, before the days of big companies making MMO's like SOE and Blizzard, we had much smaller MMO spaces being built by single individuals in their basement if you will. One such game I can call out by name is called Odyssey Online Classic. It was built completely in Visual Basic and was something I played with other people in the early 90's by running a server off my computer that people could connect to with their own client. It contained a tool to do your own mapping (building the world) and scripting (creating interfaces, spells, rules, etc). In 8-10 years or so down the line from now, who is to say we couldn't make something like that on an individual basis? Maybe it would take more years, but that stuff simply doesn't glare out to me as impossible things.
There are things to be concerned with in the shows plot or dialogue but I don't believe this is one of them. Kirito's lone wolf Gary Sue situation is definitely something that I can understand being a point of dragging people out of the experience. The aforementioned things though just sound like trying to keep finding things wrong with a show you (not you specifically Jintor, but people in general) already don't like.