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One 'issue' I've noticed with Dystopian Wars is it seems very easy to reach a point where you have 5-15 points remaining in a list and nothing to spend them on. Is this true for other people, and are there any other suggestions to avoid it?

There's not much you can do about it.
Sometimes there's an MAR you can take for a cruiser or two but most of the time there's nothing you can do.
It's a shame but them's the breaks...

As a follow-up, is it irrational to be bothered by being 5-10 point short in, say, a 500 or 1,000 point list?

Not at all unreasonable, but no all that game changing. No "official" points filler right now, but there WAS some in the Armoured Clash rules that could be home ruled over into DW.

Other common homeruled uses from the forum is an "Ace" TF pilot. Basically gets something like +1AA for that one token and becomes the last to be removed, or a MAR or something (I believe the notes for it are in the Campaign rules sticky on the General discussions page).

One that my group came up with is a minefield for the one short. Basically you pick a point on the board where you're recon/whatever managed to get a minefield down in. From that point you roll D6+3 mines and place the first on your chosen points. The others are spread 1D6"+scatterdice from each subsequent mine.