Is it possible to get all the codex entries?

There are a few that aren't unlocked depending on the world state you have and the race of your Inquisitor

for your Inquisitor it only unlocks the one for that character (Adaar, Cadash, Lavellan or Trevelyan)
also one depending on Ferelden's ruler Alistair or Anora (you unlock both if Alistair is still a Warden), if both rule together you unlock only Alistair's
Loghain also only unlocks if he's still alive, but only if he is the Warden contact

you might also want to check the wikia page with a completed playthrough and jot down the ones you missed and where or how to unlock them

Gotta catch em all

Hmm... there is also the Well of Sorrows decision. It has been a while, but if I remeber that right, one can get the codex entry on the list, but the real 'text' only appears if Inq drank themselves. 'Tis a bit dissapponting.

Are you referring to the "untranslatable Eleven text" codex?

Is there a way to see all the codexes you have opened over all the games you've played, or is it only the ones you've opened that playthrough? I haven't been able to find any way to see every codex I've opened so I can't tell what I might be missing in the playthrough.

It would be. I've come so close a couple of times, it would be nice to have them carry over...it just starts to feel like a waste of time collecting them if it isn't recorded which ones you already have.