Should different TeX implementations (e.g. MiKTeX's and TeX Live's) produce identical DVI files?

TeX is concerned with typesetting on a physical medium (eg paper). For Don identical output means a visually equal look and any user-level calculations are exactly identical (which is why you can't get at some internals of TeX and use their values as they might differ from installation to installation). This means that line and page breaks are supposed to be exactly at the same point. However he deliberately used floating point to calculate parts of the glue handling (in a way that it can't change line or page breaks) but when writing to the dvi file the resulting exact positions of the characters may be off by a tiny fraction.

To answer your explicit questions:

Q1: that is really showing what is explained in the TRIP test manual (the part that you cite in Q3).

Q2: no bug (because of what is written in the TRIP test manual)

Q3: not sure what is confusing about that statement. Note that "glue setting" is when finally determining the exact spots in the dvi file, when glue is used inside TeX, eg to determine line breaks it is still used with fixed point so there such differences will not show up.

Q4 you can't by looking at the dvi file (which the trip test doesn't do afaik). I dont think you can even by looking at the "Completed box shipped out" data without masking possible rounding errors in the (glue set ...) parts shown there. But that masking is possible and all other parts of the symbolic output display will be exactly the same and that is what we, for example use in the LaTeX regression test suite to compare output after changes made to the LaTeX code.

For web2c, I documented why all the differences are considered acceptable in web2c/triptrap/README, that is,