Composite Video on the NES: Why's it so wobbly?

It turns out which scanline counts as "first" depends on whether we're talking about SMPTE 170M (analog composite video) or Rec. 601 (digital composite video). Per the specifications, in 170M there are half lines but in Rec 601 there aren't.

As far as I understand it, the missing cycle at the end of the pre-render scanline means that the first scanline will start a cycle early every other frame. When this happens, that scanline will be drawn one pixel to the left of where it should be. In practice, this typically causes the first few scanlines to get skewed slightly (you can see this at the top right corner of your Mighty Bomb Jack screenshot) but I don't know enough about NTSC decoding to explain why this happens. This is more noticeable if you can get footage of the system displaying tiles on the top of the background, rather than the plain blue background at the top like your Mighty Bomb Jack screenshot has.

That is correct. The PPU does the memory fetches that would be done for that line, but no pixels are rendered.

For details: https://www.nesdev.org/wiki/PPU_rendering

Also, RGB PPUs (with the exception of the RC2C05-99 found in the Famicom Titler) do not do this, as they don't have to contend with a colorburst.