If you manually set the ISO speed to 400 or less, the blue should go away. Unfortunately that means you won't get the amazing low light ability. My One is much worse. It has a pattern that's visible whenever it's in low light. Not really a pattern actually but more like a macro of a tabletop or something, in the blue hue like yours, or sometimes in purple. It's very visible in every low light shot I take with Auto ISO. It goes away if I kill the low light capabilities by selecting a slower ISO, 100 or 200 looks best. It's not unusual for a ridiculous ISO speed like 1600 to exhibit both color shift and lots of noise, like your photos.
If you wonder how bad it is on yours, lay the phone on a table on its back with the camera on. The screen should show you any color shift or noise/patterns that your phone's sensor is causing. Make sure you have it on Auto ISO before you do this.
I suspect it's a problem for most HTC One's. Maybe even all of them. If so, it's not a defect but it is an unfortunate side effect of HTC's quest for the best low light ability.
I also hope the next software update fixes it.
edited to add: This image is an example of what my sensor looks like, I laid the phone on its back and snapped the shutter. This shows up in every photo I take on the auto setting in a low light situation overlayed on the photo itself. I still think it's an amazing camera that takes great pictures in most lighting conditions, just not low light or harsh sunlight in my case
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Here's a photo showing the problem on a picture.
---------- Post added at 04:15 AM ---------- Previous post was at 03:39 AM ----------
Just to show that the camera is capable of making great images, here's the same bird, same location, same phone/camera, but better light. This photo is at ISO 320, on Auto. The purple ones above are around ISO 1600, also on Auto.
