What is the correct pronunciation of 垃圾?
(As I very recently learned)
The standard pronunciation for 垃圾 is lājī in the PRC and lèsè in Taiwan
An obvious question to ask is Why? Although I could not find an authoritative source, I have seen a number of claims that are very similar to each other. I'll refer to the talk page for 垃圾 on Wikipedia:

标准普通话是读laji，以前的国语是读lese，因为垃圾本来是在方言中首先使用的，所以现在南方各地的方言里还是保留着当时的发音，后来普通话吸收了这个词，但是读音根据形声字的一般发音规则作了改变，所以读音改为laji，而台湾依然保留了lese的读音。--3dball 21:01 2006年1月13日 (UTC)
垃圾一词在宋朝就有, 见吴自牧的梦梁录. 本为lese, 是共产党有边读边念错变成laji --Bobbybuilder 2010年12月6日 (一) 18:36 (UTC)

An translation I've taken a few liberties with:

A: The reason that [on the mainland] it is read laji but [in Taiwan] it is read as lese is that the word was originally from a dialect. The word was borrowed into Mandarin, but the standard pronunciation eventually become laji based on a (mis)interpretation of the characters' phonetic components.
B: The characters do show up in Song dynasty texts (e.g., ...), but it was the CCP who mispronounced it.

Other important evidence:

The wiktionary page shows pronunciations in many dialects. If the characters are cognate, it's always an &quot;s&quot; for the second one.
The characters don't show up in Song dynasty 广韵 book of pronunciations (e.g., probably new characters), although they do show up in other Song dynasty texts.
The word was written with different characters in different texts; the standard was established rather late.
laji did not show up as the dictionary standard until PRC times.
In Cantonese, it's laap6 saap3
In Shanghainese: [lɒ²²ɕi⁴⁴], Suzhou dialect: [lɒ³¹⁻²²si⁴⁴]