The Library / TV Shows directory needs a “little” maintenance. The genius who to came up with the current sort needs to have the location of his/her head checked … its location has shifted.
To make it simple, the correct order of sort is:
Season # … Top Order
Episode #
Recording Date … Low. Order
For we mere mortals this is just Common Sense.
For Tablo this is apparently Rocket Science.
You have to remember this was the app that got released where the 3 locations where the channel list existed were all sorted a different way.
I am fine the way things are, all I really need is recent recordings at top. I only save 3 episodes of everything so season, episode and all that really don’t matter. So your Low recording date above would be my top main choice. 
Since you only save 3 why not just output them in random order. But for all the rest of use maybe some logic and common sense is needed.
I agree that this sort order is important, but not all users necessarily want it sorted the same way. This is one of those things that I would like to see as a user preference that could be saved in the settings somewhere.
BTW, I like it sorted that same as you, season > episode > recording date.
Why not start by doing it like the legacy app. And all those wishes can be accumulated in a wish list called the “coming soon” list.
Some of us are saving series to build a library. I have one show with 222 recordings and growing. Others are in the 50+ range. A single season is likely to have 20+ episode. See my point?
To zippy’s point, each TabloTV app seems to handle sorting completely differently. Some are newest season and the older ones are below. Some have first episode at the left building to the later episodes to the right. Some have this reversed.
I think Tablo tries to cram way too much information in the recorded series episode screen. Season, Episode, Title are all ones I think should be a little more noticeable. I have little interest in the recording date or times – although the information is great ot make sure I’ve recorded the entire show/movie. Since there’s a popup before you’re able to play a show, this would be a great place for the description.
But again, none of the apps seem to have a set order to how things are. It’s very frustrating!
I would like to be able to set the default sorting order for my Library to A-Z, instead of the default “recently recorded.”
The roku gen 4 app should have sorted the library like the legacy(A-Z). And any other method an add on option. I would think it would be harder to get legacy users to migrate if it’s sorted any other way.
Recently recorded is different.
Some apps have a default “recently recorded” view within the shows/movies section. You can switch to A-Z, but it is quite annoying to have to do this. One of my first comments about this was that it should default to A-Z in those areas.
It’s like they’ve got entirely different teams working on each OS without any idea of how another’s layout is.
On roku the recently recorded menu is totally messed up. It should list each episode recorded and descending from newest episode to oldest.
Same here for Roku-but also on Android, some seasons are ok (as used to be in order by episode number) and some seasons in scrambled order, this is true for both my Roku’s and android.