Filling nail holes in door frames for clear varnish finish

[Matteo]

After some very helpful advice from theshedman on painting new plaster, I joked about needing advice on doors. Now it seems I DO need some help so I hope someone here can...

Our new house has untreated beech doors/frames. The door frames, naturally, have some nail holes which we'd like to fill.

Unfortunately, we got conflicting advice about WHEN to fill those holes: some said before varnishing, some said after.

Just about all the advice on line seems to say AFTER but this is directed to people who want to stain the wood - this makes sense since I can assume that wood stain will not stain filler the same as wood and matching stained wood with coloured filler is easier.

There doesn't seem to be any advice regarding filling in holes for a clear varnish finish.

The problem we've discovered is that having applied a beech coloured filler (which you could scarcely see against the raw wood) then applying the clear varnish (which has resulted in a slightly darker, more golden finish) on one door, is that the filler shows up in lighter spots/patches through the varnish.

Does anyone know:

a) how to rectify this problem
b) how to prevent the problem occuring with all the other door frames that my wife has "efficiently" filled already in preparation for varnishing.

Am I also right in thinking that we should remove excess filler with a scraper or sharp edge, rather than sanding?