There seems to be 2 major issues with the Slingplayer app when using the Lightning to Digital AV Adapter. I'll break them down.
1. Overscan (See images: Overscan 1 and Overscan 2)
This refers to the black border on all 4 sides of the image. This is an issue with all third party video apps.
SLINGBOX, HERE'S HOW TO FIX IT!!!
There is a simple change that needs to be made in the code. Here is an excerpt from http://www.iphonelife.com/blog/87/tv-display-output-why-does-your-picture-have-black-border-and-how-can-it-be-fixed
All you need to do is, upon setting up the external screen (via, say, if ([[UIScreen screens] count] > 1) externalScreen = (UIScreen *)[[UIScreen screens] objectAtIndex:1];), set the overscanCompensation property of the above UIScreen instance to UIScreenOverscanCompensationInsetApplicationFrame (=2). It'll entirely get rid of both the border (overscanning) and image quality-deterioating scaling.
I'VE PROVIDED DETAILED STEPS ON HOW TO FIX THIS ISSUE. I'VE DONE THE APP DEVELOPER'S JOB FOR THEM. PLEASE FIX IT ALREADY!!!
2. Aspect Ratio (See images: Aspect Ratio 1, Aspect Ratio 2, and Aspect Ratio 3)
This refers to the image being "squished" from the top and bottom. This only happens with the Slingplayer app when using the Lightning to Digital AV Adapter. This is not an issue with any other video app.
I've spent hours researching this issue (Slingbox forums, Slingbox phone support, and web searches). There is an error in the code of the Slingplayer app, but unfortunately I do not know what the solution is. This is not an issue with the TV, iPhone, or adapter. This is a SOFTWARE issue with the Slingplayer app.
In the image Aspect Ratio 1, you can see on the left the direct HDMI connection to my Dish Network box. On the right, you can see the "squished" image from using the Slingplayer app for iPhone with the Lightning to Digital AV Adapter connected to a second TV.
Note: These issues have been discussed in other posts on this forum. (https://community.sling.com/thread/24994?tstart=0 and https://community.sling.com/thread/26107). They have been INCORRECTLY marked as answered. Therefore, I have started a new post for these issues.