Legionseagle made a good start but I thought it would be fun to make a collaborative list of all the homages and shout-outs in The Abominable Bride to canon and other Holmes versions
(I'm seriously considering making a list of all the stories that were directly quoted and giving it to Sherlock fans who haven't read canon if they'd like to hunt 'em down in a reverse Easter egg hunt.)
Anyway... here's what I've got in no particular order. Sing out in comments
Pretty much the entire beginning: Study in Scarlet
Blue Carbuncle: Blue Carbuncle
Mr Melas: The Greek Interpreter
Possible dual coffin: The Strange Disappearance of Lady Francis Carfax (hat tip: legionseagle)
Train and Reichenbach scenes are taken from Padget illustrations
Much of the set dressing and mention of Senora Ricoletti: Musgrave Ritual
Deducing from a single raindrop, "Which is it today?": Sign of Four
Viennese alienist: Seven Percent Solution (hat tip: tiggerallyn)
Boot slitting, Irene, "Crack in the lens": Scandal in Bohemia
chanting secret cult: Young Sherlock Holmes
orange pips: Five Orange Pips
Sir Eustance Carmichael Brackenstall murdered at home during a break in: Abby Grange
"The fair sex is your department": Second Stain
"The dog one": Hound of the Baskervilles
In the headlines of the first set of "Bride" newspaper clippings was "Sea captain found dead": Black Peter
Legionseagle, where's the Rathbone reshoot?
I would have sworn that "regulation tread" was a quote, but I can't find it. The bit about bad/missing breakfast is also a homage, but all I remember of the original quote is "love romance" and googling "Sherlock Holmes" "love romance" gets... interesting... results.