Well, on any keyless wind instrument, more shape and flats means more gnarly fingerings. On a recorder it also means the notes are less clear, because forked fingerings have that effect in a tubular instrument, but not in Coda!
On a sax or clarinet, we're supposed to practice scales etc in all 12 keys. I've never been that disciplined but I do try to play songs in a number of different keys on the sax. And some songs really are good training for playing in all 12, like "The Rose."
On Coda, some keys are really a lot of work. I'm not a fan of playing in Eb, en though it's a fairly common key. It just feels clumsy under my fingers. But really it's all about getting the discipline to practice in all keys.
I've started practicing a drill I used to do on sax. Starting on middle C I play a major arpeggio up to high C, so c, e, g, c' then a semitone down and play the downward arpeggio in B major: b, f#, d#, B then down another semitone to Bb and arpeggio up, etc, until I've done every key and end on low C.
Like all drills, you have to start *slow*, like quarter note tempo. Or do a similar thing with scales instead of arpeggios. It's tedious but it helps. Even on a keyed instrument it's a challenge but on an instrument with no keys it's real work.
That's more than you asked for, but for me it all comes down to fingerings.