I've notice the connection flipping between 3G and H & H+ much more since updating my UK SNote with the official Samsung 4.0.4 UK GT- N7000 firmware through the 3 network. I know there's nothing wrong with phone it's like a member who posted here said, the second I go use the browser, or email app the connection flips from 3G to H then H+, especially more so if my signal bars are low (displaying 1 or 2).
I thought as others here had that maybe there was a problem, or corruption with the phone now it had been updated, so I reset and recovered the phone again this time using Samsung's Pc software 'Kies', installing everything upto ICS 4.0.4 firmware like it had been received this way out of the box.
My provider is '3', and I know that when I'm in a strong signal area the flipping between 3G to H & H+ is either none existent, or very minimal only really showing itself to do the change when the screens awoken from sleep mode, briefly showing 3G then it's straight to H/H+.
But at home because I'm on the fringes of a 3G signal, with no 2G transmission from the '3' network anymore to support my area, this seems to be the conditions when the flipping over of 3G to H/H+ changes constantly, only choosing to upscale the connection when absolutely required, I'm guessing this is a kind of 'user contention' system that the 3 network might be employing, evoking it as 4.0.4 was release through there network , now especially with the 'all you can eat' data tariffs and large sales of the Galaxy S3's
All I can say is, this seems to be how things are working for me right now, I'm sure that over time signal strength's and connection speed will only get better, now that the likes of iphone 5's, and SNote 2's will be soon here to push them.
Regards