[Rhapso]

I really really wish they would call it "apparent mass". It is entirely an observer effect. Its entirely "that ship throws propellant out the back but they don't end up going as fast as Newton thinks it should, so it must have more mass than we think"

[whatshisface]

If there are many objects moving in many directions, you won't be able to find a reference frame in which the mass of the system is equal to the sum of the rest masses of the objects.

[Rhapso]

correct. This is not a contradiction.

A reference frame is definitionally a point from which you would measure an "apartment mass". The rest mass isn't relevant to a reference frame where that mass isn't at rest. This is true at all scales.