I'd say either those components shown in solderside.jpg were replaced
at some point, or the person doing the hand-soldering wasn't
particularly competent. More likely the latter since the signs are
there at every pin that's a hand-soldered part, as far as I can see.
It doesn't look like re-melting as you suggested. So it's not that
solder has escaped from the joints, it's simply that more was
originally put on it than the rules of good workmanship call for.
Look at D910 (a bit further to the right on that photo) for an example
of good work. (I think that one is the wave solder machine at
work...)
The brown gunk looks like flux (rosin) that wasn't cleaned off. The
solder joints have more solder on them than they should, but not so
much that you'd get solder bridges as far as I can see. Excess flux
can cause corrosion and leakage current, but I don't see corrosion
here and some leakage is not all that likely to be an issue for a
power circuit such as this.
It probably wouldn't be a bad idea to re-heat those joints with a
piece of Solder Wick to suck up the excess solder, and then clean off
the rosin with a suitable flux remover. (Unfortunately the good ones
are all Politically Incorrect. Maybe acetone would work, I haven't
tried lately.)
The dark spots on the board seem reasonable. Those resistors are high
power wirewound units, those get *very* hot in normal use. Raising
them -- and high current diodes like D907 -- off the board is a
typical trick to get better cooling. The radiated heat tends to
discolor the board at some point, that isn't necessarily an issue.
Something to look at, though: on the "solder.jpg" picture I wonder
about the funny rings on the right solder joint of R923 and R924.
That may just be a shadow, or it may be a mechanical problem in that
joint. It wouldn't hurt to find joints like that and re-melt them.
paul