Tonight is the first time I've ever experienced a problem with Netflix. I too am getting a "connection error" from my Roku box while in Netflix. I'm connected via wired ethernet, have a 10mbps network, and all other Roku channels I subscribe to seem to be working fine. I've rebooted my box, checked my settings, I'm at a loss. I've read other posts stating problems w/ netflix yesterday, but they all seem to say they're back up and running properly now. When I go into Netflix it takes way longer than normal to retrieve the home page. My IW que only populates maybe 10 poster views of my movies and all others are blank. Same for search. Genres, and all other categories are totally blank. Not even the outline of a movie poster. Within 15 seconds of moving around the que, the connection error appears and all I can do is return to the Roku channels page. When I re-enter Netflix, it loads quicker, but I get the same results.
We have been having connection issues since Friday night. It sounds exactly like your issue. While scanning through the queue, the first few poster photos show, the others are just a gray box with a dotted circle arrow in them. In many cases, we couldn't even get the search or other choices to work at all. Last night, it was better, but when scanning through the possible choices, I kept getting the "connection error". I checked the connection on the roku box, even re-setting it up. I re-booted the box, all with the same results.
We're currently running with a wireless connection, I had planned to run a wire to the roku sometime this afternoon to see if that helps.