Business Case (I know how you PMs love these):
The current CB 1902 implementation is going to make this conversation part of our helpdesk script:
“What screen is the app on?”
“Can you move that window to the monitor where X is showing?”

“No, not that one.”
“Nope, still don’t’ see it”
“Ok let me reconnect in full screen, please accept the prompt again.”
“No no no, don’t hang up the phone, that’s not how this works.”
“Ok, you should see a prompt to allow me to connect.”
“Nope it’s there, trust me.”
“Got it, thanks. Ok, let me move that over here.”
“Ok, I’m going to reconnect again so I can see what’s going on.”
Click
“You just hung up, didn’t you?”

This is going to waste time on support calls and leave both sides dissatisfied with the entire experience. In turn, customers will continue implementing other third party remote control tools. Remove Viewer was absolutely a selling point for ConfigMgr and was one of the features that lured us away from our previous solution.

Solution:
1) The ability to select any single screen connected to the remote device in addition to the current all screen view.
2) The ability to change monitor selection without having to reconnect the remove viewer.

Notes:
I could probably live with automatic reconnection provided that the admin stays in the Remote Viewer app at all times and doesn’t need to retype anything (device name/credentials) nor the end user re-accept the prompt if one is configured.
In my dreams the ability to pick a single screen is built into the full screen mode. In full screen mode the admin clicks a button that overlays each monitor with a number and an outline. If this sounds like display setting’s ‘Identify Monitors’ that’s because that’s exactly what I’m thinking of. However, don’t stop there. In that identification mode make the monitors selectable such that when I click on one it immediately becomes the single monitor I’m connected to.

I would like to thank Microsoft to allow their customers to share new and innovative ideas and I would like to present mine from my experience as Desktop Management Engineer in my company.
Initially we were using a comparative tool called LANDesk Management Suite and on the beginning of this year we have moved to SCCM 1511, since then I had received many complains about remote control comparing to the past experience.
I really like SCCM as a whole and I think it is really good tool and really nice features and constant updates, but not the remote control.
I have known many companies using SCCM with 3rd party remote tool like DreamWare, SolarWinds, LANDesk,…etc. because of the SCCM remote limited options and performance issues.
The below is the list of some really good features to have in SCCM remote control tool:
1- Ability to remote control the machine with permission even if the no user is logged in. sometime this option is really required when the client has a problem with logging in to the machine like if the machine is out of domain, the Helpdesk guys are not able to control the machine and rejoin it again considering unattended remote control option is not allowed because it is without permission for security reasons.
2- Ability to configure remote control or remote view access for SCCM users in which some users will have view access only and others to have control access only to the same machine.
3- Multiple Screens switching in which the user can move between screens to make it easier in supporting the client.
4- Screen Quality control when remote control the machine. For some site the speed of the network is very slow, the remote control will be very slow and will cost time to service the client.
5- Option to ask for Reboot.
6- File Transfer loading bar to show the progress of copying a file and remaining time.
7- Current logged in user name to the remote machine and the IP Address as well while remoting a machine and it is good to place them on the top of the remote control green bar.
8- Having a web console for remote control will increase the likability of SCCM.
Finally it really be appreciated to consider the above which will improve user experience and will make customers to like and to use SCCM remote control more than any other tool.

I have previously reported this as an issue in the Connect Site but was Closed "By Design".
So here is the original idea that was filed:
There is a serious issue with the way Client Settings are applied when you need to provide different levels of remote control privileges for specific Users/Groups on Collections.
For example:
Let's assume we have the Collection of Devices named "Windows 8.1 Clients", the requirements for remote control are:

1) The "Helpdesk" Group of users should have the ability to "View Only" via remote control the client devices.
2) The "L2 Support" Group of users should have the ability to "Full" remotely control the client Devices.

This cannot be achieved in the current version (2012 R2), whatever way you try to do it you end up with all of the above groups having the most strict setting!

Original Link in Connect: https://connect.microsoft.com/ConfigurationManagervnext/feedback/details/1288733/sccm-2012-r2-inability-to-set-multiple-remote-control-privileges-to-collection-s

Similar idea in uservoice but not so detailed: https://configurationmanager.uservoice.com/forums/300492-ideas/suggestions/10694637-allow-multiple-remote-control-policies-for-a-singl

I hope this gets enough votes to become implemented as it is a feature that has been asked numerous times from my clients and trainees.