The battery on my p4 doesn't align perfectcly with the body. Anyone else have this issue, or just me? the top is good, just the bottom isn't right.

Bottom of mine looks exactly the same.  I was worried at the start but pushing in the top clip on my and trying to take the battery out.   Lower clip on mine holds tight so I am not worried.    Try pushing top latch down and removing the battery to make sure your lower is holding well.    Don't go nuts but a few tugs should prove if it's connecting inside like it should

it is an High range Tool in the sky at 10000 feet the tolerance is okay and the tanks have no leaks.
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The gap around 1mm is normal and it will not influence any flight characteristics since the battery is already locked in the tray.