1900's popular expressions, slang...

Absent-minded beggar...
After you with the push
(ed: being polite to someone who is pushing and/or rushing)

The call of the wild
Crazy as a bedbug
Have bats in one's belfry jdj: and bees in one's bonnet?
To go over something with a fine-toothed comb
A dastardly crime jdj: Two from A. Conan Doyle, perhaps?

Muckraker (ed:meaning exposer of unpleasant things first used by Teddy Roosevelt) jdj: Nelly Bly is my personal favorite :] , but did most of her work in the 1890's

Dyed in the wool...
To face the music
To get one's bearings
More to something than meets the eye
Traffic is at a standstill (ed:1905!!!) jdj: not surprising at all, without traffic laws.
Get off my back
How's tricks? jdj: this is so flapper-like, but I wager a vaudevillian coined the phrase, and meant it literally.
If it isn't one thing, it's another
Is everybody happy? jdj: to be slang, the expression would have to be ironic. Maybe this was a famous line from a novel or play, just before all hell broke loose...Or of course it may have been a song title. Any thoughts?

Keep your shirt on jdj: yeah , ya ya Bowery boy....
Let the good times roll jdj: sounds early but I believe it
Long time no see
No harm in trying
Pardon my French
He doesn't have a pot to piss in
Search me...
That's all there is, there ain't no more
That's the ticket jdj: so good we brought it back
Something is pie-in-the-sky jdj: was it Freud who spoke of 'castles in the air'?
You get my goat!
You'd forget your (head) if it wasn't screwed on jdj: some say the teenager hadn't been invented yet but this sounds a lot like 'Dear Old Dad!
Someone is a big-shot
To get blotto (drunk) jdj: adding to the 257 other synonyms already extant
Someone is fit to be tied
The graveyard shift
To go slumming jdj: originally used referring to social workers

New words added to Collins Dictionary:

Labour Party
Fingerprint jdj: true progress. Did Holmes know about fingerprints?
Teddy Bear jdj: 'Teddy' for Theodore Roosevelt. I forget the story behind this and am too tired of the ex-president to look it up.
Tarmac
Fifa
Sinn Fein
Suffragette
Allergy
Borstal
Jazz

Thanks to Larry Belling at Writer's Dream Tools.