This new update should alleviate some of those issues. The update brings new features and improvements to the service as well as bug fixes. March 14th Karen Tong posted information on the update via the Skype Blog writing, "Since we launched Skype for Xbox One* in November, we’ve been hard at work improving the living room experience for Skype users. Today we are excited to announce the first update to Skype for Xbox One, which brings several new features . . ."
Using Skype on your Xbox One will now see improved chat, streamlining messaging between devices. There's also the new ability to filter your contacts and a new tutorial that will instruct first timers how to use Skype for the Xbox One. Plus there's new emoticons from "Marvel’s Captain America: The Winter Soldier", cool beans.!
Skype is available for Xbox Live Gold members only. If it's a service you enjoy having on your Xbox One than keep giving Skype feedback and we'll see more improvements.