Disclosure: I'm on a Galaxy S4 - smaller screen than the Note 2
I definitely know the feeling of browsing a "mobile optimized" site and still feeling like I have to use a toothpick to successfully "click" on certain UI elements... That said, I really did not get this feeling when browsing the SE network on my phone. The only thing I found annoying is trying to click on my username inside that top dropdown menu to get to my profile.
Lets be honest here for a second - you don't really have to click on that little arrow to trigger the dropdown, do you? Anywhere on the box containing the arrow works as well... Or is it that human fingers just touch the whole box in any case... not sure if this is the case on your 60m2 screen - but I'm pretty sure the average person's finger will still cover the entire square.
I actually almost never click there in anycase (I'm just saying)... I have a bookmark to my profile page and just navigate from there...