I'm sure others have found/will find many more, but these were two bugs I noticed while playing as Advent Loyalist in the latest iteration of the beta.

1) (Graphics) The icon for the Aeria's Mine Control ability is Incendiary Rounds.  Now, I'm no expert on telepathic control, but I doubt it involves fiery missiles.

2) (Gameplay) The Solanus Adjudicators have...a bit of a problem.  Twice in my current game, when my fleet has left a grav well, two Adjudicators have apparently remained behind.  However, looking around the gravity well doesn't show them, and when I click the icon to zoom in on them, my view is whisked away to some far reach of the galaxy where I can't even see the system I'm playing in in any direction.  As far as I can tell, the guilty Adjudicators have ceased to exist, although the still use fleet supply.  The only workaround I've found for this is to scuttle them and rebuild more, but it's quite annoying.  I have not thus far paid close enough attention to all of my Adjudicators during any given battle to see where the things actually go.

Also, phase jump logic seems dodgy at present.  Aside from the aforementioned Adjudicator issue, I've sent a fleet out from a grav well and had it jump in with the ships strung along the phase lane from about the edge of the gravity well to about twice the well's radius away from the planet.  It was only once, though, so it's possible some other factor was at work.

Loving the Advent!  Rebellion's definitely shaping up to be a great game.