In the previous post, I came up with a final plot showing the pointing offset was, on average, not significant, even in the ATLASGAL overlap zone. So why did the ATLASGAL group infer a net pointing offset? The problem is probably one or two fields with a slight pointing offset, but a huge number of source.  l=1 has an offset of the right sign and is the single most source-rich degree in the survey, with 368 sources.

This figure shows the v1 vs v2 source locations in grey, their average and standard deviation in green, and the cross-correlation offset in red.  The plot is somewhat difficult to interpret, but it appears that the v1 point sources are systematically more shifted to negative longitudes than v2, and the point sources more than the maps themselves.  There may have been some reason sources were systematically selected at more negative longitudes in the v1 catalog; around Sgr B2 there's a lot of structure that had to be decomposed somehow but was not necessarily "source". One thing to note is the reversal in left-right (in pixel space) vs the positive/negativeness in longitude.  The above plot is correct (negative longitudes, as shown on the plot, are "right" in images), but most of my other plots have the X-axis flipped. In the end, after spending two weeks hammering my head against this, I find no clear evidence for an offset  between the BGPS and Herschel or v1/v2 data overall or in the ATLASGAL fields.  In any individual field, that statement is not necessarily true. Despite the strong statistical evidence, it is really hard to be really sure about sub-pixel offsets, since the "model" image is never perfect.  I think we can safely state the ~1/2 pixel offsets (~3") but I just don't feel confident about numbers below that range for ALL fields.