I am STILL having this issue, and the reply I shared in the last couple weeks with additional issues was removed. "Solution" linked is for Dell brightness functionality and I have not seen any improvement with the update; if anything, in the last week my user experience with GoToMyPC has gotten worse.
I am on a laptop running Windows 10 Pro, remoting in to a iMac running OS X El Capitan 10.11.6. In addition to shift commands not working as mentioned in OP, I am experiencing all kinds of wacky issues with shortcut keys. The Windows key is used in place of the Apple key for shortcuts (ie, Windows+C to copy instead of Apple+C). Use of the Windows key seems to toggle all kinds of things on and off on my host computer: sometimes it launches Spotlight. Sometimes it activates tab browsing in Finder. Sometimes it locks me out of the Adobe program I am using. Sometimes it acts as numlock. Sometimes it turns off my arrow keys. Sometimes it changes the direction my scroll mouse steers (vertical versus horizontal). It's ALWAYS really, really frustrating.
Is this some setting that I need to correct on my client computer or is this a bug in GoToMyPC? Would love some assistance as this makes using this product quite unpleasant.