Anything relating to collars or lapels — All of these aspects of period clothes are full of pitfalls that would look costumey in any contemporary context: twee club collars, foppish collar pins, dated high or narrow lapels.
Hats, in general — No. Just forget it.
Coat styles — There are exceptions, sure, but most suit coats in ye olde days seem to have been baggy 3- or 4-button monstrosities.
Colours — It's been a few hours since we said something about how well brown, olive, and camel work as neutral bases for strong colours.
Hair — There are at least half a dozen variants on close-cropped and tight that work in every decade. Just go easy with the goddamn gel.
Materials, textures and patterns — Tweeds, wool flannels, plaids, windowpanes, herringbones and chalk stripes were awesome in the early 20th century, and some things never change.