No, that's not a ghost touching your screen--those phantom double taps and presses you may have been experiencing with your new Nexus 7 are actually a software bug. Fortunately, Google is rolling out an update to fix it today. Google's Paul Wilcox confirmed in a post in the Google Product Forums that the update to Android 4.3 will specifically address the device's touchscreen response issues. He writes:
"As a couple of you have mentioned, there's a new system update that's started rolling out for your Nexus 7s. This update does address the touchscreen issues discussed in this thread. If you're one of the people experiencing touchscreen issues, please let us know how it's going after you've received and installed the update."
While the new Nexus 7 is a major hardware update from last year's iteration, its launch hasn't been without a few snags. In addition to the aforementioned multitouch issues, many had also taken to the Google Product Forums to complain that the Asus-manufactured tablet had GPS issues, where the tablet would remain in "search" mode and stay locked up for up to half an hour until it could properly pinpoint the device in its current location.
There's no word on whether this particular software update will address those GPS performance issues, but users who have received the software update are leaving positive reviews. You can check to see if you're eligible for the update by heading to the Settings menu, scrolling down to the very end and selecting About Phone, and then tapping System updates.