I love the app, but there is one thing I'd change to perfect it, because I'm a heavy label user:

When choosing a label, there's no immediate visual feedback to show which label you've selected. This might not sound critical, but using a finger on a moving train can lead to inaccurate pressing! Compare that to the web interface: select a label, and there's immediate feedback saying "this conversation has been moved to/labelled "whatever_the_label_is".

I'd like to either see my selection invert, or a confirmation similar to the web interface.

(And agree with the OP: taking up valuable screen space with a thick border is inefficient).