I've owned my Surface Pro 2 just over 30 days; it was purchased to replace a Nexus 10 Android tablet.
Our company uses a CRM which requires the use of Internet Explorer, no other browsers will work.
Although the original intent was replacing the Android tablet, the capability and function quickly allowed me to replace my laptop with the Surface Pro 2, turning my use into one that mirrors the use of the original poster. I use the Type Cover, Docking Station, LED monitor, wireless keyboard, and wireless mouse. My SP2 is 4/128.
During my first week of ownership I could not figure out how to use the split screen function, called Microsoft, and made an appointment at one of the local stores. Similar to the OP, when I arrived they did not find my appointment in the system - there may be a breakdown in MS' appointment calendar data transfer? Unlike the OP, the MS Store had a greeter who, when he could not locate my appointment, immediately directed me to the service counter where an associate listened to my question, took me to a desk area to educate me on split screen use, and offered to demonstrate and educate me on other useful features of Windows 8.1. Mark this as a good experience for me.
The Surface Pro 2 has exceeded my expectations for hardware and functionality.
At this point the only issue I've had with the docking station was intermittent external monitor signal. I connect via HDMI adapter and cable and was using a Belkin adapter but did not experience intermittent external monitor signal when the video out adapter was connected directly to the SP2. Upon examination I noticed the Belkin adapter insulated end was larger than the port of the docking station which prevented full insertion of the cable adapter. I ordered the SP1/SP2 HDMI adapter directly from Microsoft and have not had any further problem. The Belkin adapter works fine when attached directly to the SP2 so I bring it and an HDMI cable with me for presentations while on the road.
I post this not to discount the experience of the OP but simply to state your experience may, like mine, be very good.