I can't seem to take a picture in focus. I've read things here and there about people having similar issues, but many people don't seem to have any problems. It's not user error either--I know how to hold it steady. Is my phone defective?
HDR+ can run into issues with movement, however, as you'll see in the second set of comparison images below. The people in the foreground are blurred and obscured by noise. Not surprising — as the phone has to have time to take multiple exposures.
I am also not trying to insult your intelligence, but are you tapping the screen to focus on what you are taking a picture of? I have taken quite a few pictures of people and things and haven't had any issues.
Try taking some pics outside. Most indoor lighting are not good enough for any camera phones. Some might be a little bit faster than others. But without flash on, it will be very slow and hard to focus on. The shutter lag of the default camera app is also mentioned in many reviews.
Here is what you should do: take a picture in the condition you describe in OP and open the picture, choose menu->Details. Report the aperture and exposure time here. From what I can gather, the rear camera has a fixed aperture of F2.53 (which is not that fast). Indoor pictures can often in the range of 1/15 sec to 1/30 sec of exposure time. At 1/15, your subject should stay steady. The OIS can only compensate minor hand shake of who takes picture, not for the subject movement.
I've tried camera 360 and various other cameras, but none of them have any faster shutter speed and focus speed...
From what I can gather, the rear camera has a fixed aperture of F2.53 (which is not that fast).
On the bright side though, we have now confirmed that many of the problems with the Nexus 5′s camera can in fact be fixed with a software update, and it’s likely just a matter of time before Google issues some fixes.
Can you take two pictures (one with HDR+ and one without) and post it here for us to take a look at? I'm interested in seeing the image quality.