Was Kubrick fascinated by doubles? Some of the blame can go to Burgess of course or was he saving money on props?
Here is a list of things that happen twice in the film in order of first appearance.

# Event 1st 2nd
1 Alexes Alex Mr. Alexander
2 Roles of Georgie + Dim Droogs Police
3 Korova trips Beginning After Alexander attack
4 Uses for milk Sharpens Alex up in beginning Harms him by Dim in middle
5 Tramp encounters Beating in beginning Attack on Alex near the end
6 Naked women on stage Billboy's gang rape Girl tempting Alex at Ludovico
7 Unsuccessful rapes By Billboy's gang  By Alex on stage at Ludovico
8 Bottles kicked by Alex In derelict casino Returning home in the lobby
9 Pianos In derelict casino In the prison chapel
10 Surprise arrival at Mr. Alexander's house To attack them in beginning To find shelter at the end
11 Mr. Alexander appearances As victim As attacker
12 Red typewriter In Mr. Alexander's house In Alex's Room
13 Character wearing bathrobe before attack Mr. Alexander Alex
14 Use of balls In the Alexander's mouth Pool table at Dolins'
15 Woman with mouth gagged + breast exposed Mrs. Alexander Painting in Catlady's room.
16 Singin' in the Rain During Attack During bath (when raining)
17 Penis attacks Rape of Mrs. Alexander Statue on Catlady
18 Rapes Mrs. Alexander In Ludovico film
19 Women attacked by Alex who die later Mrs. Alexander The Cat Lady
20 18 Alex lives at 18a Linear North Prison cell across from Alex's
21 Bathroom When Alex returns home to pee In Mr. Alexander's house
22 Same Beethoven picture On Alex's shade In Alex's jail cell
23 Alex walks in a big circle In record shop In prison courtyard
24 References to previous Kubrick films 2001 record in Korova 114 Serum (Dr. Strangelove)
25 Droogs go into the water Dim Georgie
26 Alex cuts someone with a knife Dim's hand In Bible fantasy.
27 9th symphony affects Alex In the beginning it's pleasurable In the end it is painful
28 Turntables In Alex's Room In Hospital at the end
29 Surprise guest in Alex' s house Mr. Deltoid Joe the Lodger
30 Deltoid's gross mouth Drinks denture water Spits on Alex
31 Deltoid appearances In Alex's house At the jail
32 Alex is betrayed by his droogs Catlady's house When they are police
33 Beethoven bust Catlady's house In Alex's jail cell
34 Alex trapped in Ludovico In Dolin's house
35 Blue typewriter In prison library In Mr. Alexander's house at end
36 Historical Fantasies Biblical in prison Ascot ending
37 Alex hand-fed Grapes in Biblical scene Food in hospital
38 Minister of Interior presents Alex to a crowd At Ludovico Center In Hospital
39 J.H. Lynch paintings In Alex's front room In living room
40 Stand up telephone Alex returns home from prison Mr. Alexander's house at end
41 Weightlifters Joe the Lodgers room Julian at Mr. Alexanders'
42 Alex's Mother Cries When he leaves his house At the hospital
43 People carried by Julian Alex Mr. Alexander

I think that by Kubrick having Alex appear in the exact same bathrobe that Mr. Alexander wore when he was attacked by Alex foreshadows the attack of Mr. Alexander on Alex. The last time we saw it there was violence and we should expect it again. It is subtly placed on the hanger while Alex is in the bathtub, but you wouldn't really notice it. Why would Mr. Alexander save the robe is he was attacked in unless he hoped to pass it on, never really believing he could use it on his attacker?

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