The ability to download audio and video for offline use and the ability to watch videos not embedded into content, like General Conference talks.

The ability to have your tabs and synced between all devices that share an account so you can move from one device to another without having to find all your spots again.

It would be great if I could group or categorize my bookmarks. I could have a group of bookmarks for the lesson I'm working on and a separate group for scriptures I've memorized, etc. It would make it easier to look for the bookmark I want in a long list.

Add option in appearance section of settings to choose whether the live tile is solid colored (current appearance) or transparent.

Make lds gospel library available as a lock screen similar to where bing cycles through pictures of the day, you could do temples of the day

It would be nice if when you enter the app there is a setting to where the screen never turns off until you leave the app like the android version.

When I perform a search, it appears that it only searches content I have downloaded.
As such, I frequently have to switch to a browser, perform a search, switch back to the app, and download what I need.
It would be so much nicer if I could just specify I wanted to perform an online search, then, if I found what I wanted, I could just click to download (much like clicking on one of my notes that refers to content that isn't downloaded yet.)

It would be really nice to have a feature (optional, that could be turned off or on) that would automatically date-stamp notes that we create. Seeing when I created a note even years later can help me remember the context under which it was created and magnifies my scripture study.

Many people use colours as a personal category system (e.g. words spoken by the Saviour are in red, missionary scriptures are green, personal scriptures are in Blue, etc.)

On the annotation page, if it was possible to filter annotations based on the colour of highlight / underline used, it could help people using this marking method to locate their personally selected scriptures.

Add the ability to put a box around a section of text. This would be especially useful if one could also underline key words within the box.
Example: I would like to put a box around the parable of the Good Samaritan but then just underline the one key word Samaritan.

Add the capability of dropping individual scriptures, talks, or other customizable selections into the collection

Include the ability to use Boolean operators in search, like AND or OR.

It would be nice to choose to either listen to instrumentals, or instrumental with vocals.

I find the swipe action requires a very vigorous swipe, on my Lumia 640 at any rate. Its a bit more distracting too. A tap on the side like you can do with the kind e-readers would be a simpler approach.

I prepare lessons using the app. I would like to be able to place the note prior to the selection. Placing the note prior to the selection acts as an introduction to the selection that is helpful for creating lessons or to act as reminders of what to look for the next time I read the selection as part of my personal scripture study.