Minecraft – What are these red lasers

Those are absolutely player coordinates — the .62 in the middle (y) coordinate is a dead giveaway. If you check your position using F3 while standing on any full block, you'll see your y coordinate always ends in .62000… (or occasionally .619999…). This is because the player's coordinates are reported from the "eyes" — the point where the camera sits in first-person view. A player's eyes are 1.62 blocks/meters above the ground.

Now, as to why they aren't accurate, I couldn't say. My best guess is that it's related to the "spawn radius" in SMP. When you die (or log in for the first time), you don't spawn at a fixed point in the world; there is about a chunk-sized area in which you can appear. It's possible that, when a returning player is added to the world, they are either initially placed in the spawn zone before being moved to their real location, or alternatively that the spawn radius is applied to their entry coordinates and reported in the log, but discarded before the player fully enters the world.

Update: A bugfix listed in Notch's blog post on the changes coming in 1.6 supports this theory:

• Fixed players spawning in the wrong location and quickly lerping to the correct location

("Lerping" refers to linear interpolation, the type of math which controls player movement.)

In server.properties make sure Nether is enabled