I like the inclusion of the toggle for customizing your "linage" in the character builder, that way if you wanted the default for the race, no needing to click and select things.

I believe the sidebar from that section of TCoE that added the "custom linage" race needs to be added though as an available race and not as a homebrew race that the community has made.

Also when you take the fighter initiate feat there is no option to select which fighting style you want. So if you took the unarmed fighting style you then also have to add in a custom weapon to indicate your new unarmed damage. Or add in the blind sight 10ft got the blind fighting style.

I believe it's the same thing with the Eldritch feat (the one that lets you take a warlock Eldritch invocation.

As for the player app, I dislike that to customize my character I first got to load it in the app, then click open the navigation of the different sections so I can select "view on the website" just to change things about my character. Which includes being able to open the edit function of the character itself.

Adding Customized Linesg is on the list. It’s not as simple as it sounds, and they learned about it less than 3 weeks before the launch of the book. 

fighting initiate and eldritch initiate are both addressed in the first post of the Tasha’s support thread. Currently there is no way to add fighting styles or eldritch invocations through a feat without breaking the sheet. It’s on the list for the developers to address. So for the moment those feats are just placeholders.