I have also noticed bugs with and had issues with iOS 8.2 on my iPhone 6. Particularly with the the Music app.
Initially, after updating my iPhone 6 to iOS 8.2, it seemed to be working fine. However, then I connected it to my computer (Sony VAIO running Windows 7) via USB cable because I wanted to transfer new music from my iTunes library to my iPhone. My iPhone, before I connected it to my computer, had about 5000 songs on it. However, after my iPhone 6 synced with iTunes, all of a sudden the amount of songs on my iPhone went down to about 2500 songs. When I looked through the Music App, I realized that only the music I had purchased from iTunes remained on my iPhone, while music ripped from my CD collection had somehow been deleted. I ended up having to transfer my whole iTunes music library to my iPhone again! This issue has to have something to do with updating to iOS 8.2, because it has never happened to me before, and iTunes hasnt been updated lately, and is running the latest Windows 7 version, iTunes 12.1.1
After finally transfering all my music back on my iPhone again, I then started noticing a major bug within the iPhone Music App. The incorrect Artist Info is displayed for many songs I purchased from iTunes. For example, I have the album "My Everything (Deluxe)" by Ariana Grande on my iPhone. Only one song from the album, "Love Me Harder", is by the artists "Ariana Grande & The Weeknd" and supposed to display as such in the artist info section in the music app. However, 13 of the 15 tracks from the album all incorrectly display "Ariana Grande & The Weeknd" in the artist info for each track in the Music App (the exception being the track "Bang Bang" which actually does display the correct artist info for that song). All these songs display the correct info on iTunes, and I even tried removing the album, and then retransfering it back to my iPhone, to no avail. This bug occurs on many tracks and albums I've purchased from iTunes, but only in the iPhone Music App, and only started after updating to iOS 8.2. Tracks ripped from my CD collection seem to be unaffected by this issue.