I've noticed some issues with the xbox part aspect of the game. Trying to start one while in the game is almost pointless since the party sometimes need to be snapped. While leavening the party there is also a chance that your fire team members will not be able to hear you when leaving the party while in the game. This doesn't happen all the time but it is disturbing. On love streaming I tested using the Twitch app that is on the Xbox. There were issues keeping the stream. To test this I played another game and tested the stream quality there. Was fine. I do know this is a Beta build but giving my feedback. The Crucible also had some issues with friends lagging out before or after the match. And having to join a friend through their gamertag instead of a "join fire team" option is making too many steps as well. Ruins the "flawless" joining so mentioned.
They are aware of the issue with party chat. They know how to fix it. Just a matter of time before it's rolled out. They also said to avoid the problem before they fix. Start a party before starting up the game. Hope that helps.