What does “show some (a little) leg” mean in common understanding?
The information you quote from www.wordreference and www.englishforums. com is correct in describing common usage of show some leg or show a little leg. 
The picture above, from It Happened One Night (1934), illustrates a classic example of showing a little leg as a hitchhiking device. Clark Gable brags about his skill at thumbing a ride; lots of cars go by without slowing down at all. Then Claudette Colbert shows some leg and the driver of a passing car brakes as fast as he can and gives Gable and Colbert a lift.
The idiom or imagery in Dowd's sentence probably is easily understood by a large fraction of the US public, and perhaps by other English speakers as well. However,
Dowd's sentence has problems: It says Holder is trying to appear benign to put pressure on Sterling, which seems to be a self-contradictory statement. That apparent self-contradiction makes the sentence hard to understand, at least during the first dozen times one reads it.
Does [show some (a little) leg] mean to tempt a desired reaction from the other, or to reveal one’s real intention? Is it a common phrase?
It ordinarily is understood as temptation, rather than as a way of revealing one’s real intention, although when Mrs. Robinson in The Graduate shows some leg, it both reveals her intention and acts as a temptation.
Ngrams for show some leg,show a little leg suggests both phrases have greatly increased in popularity since the 1980s, so proper understanding of the phrases probably is widespread.
There are several interesting phonological and phonetic aspects of Adele's pronunciation of this line:
Think of me in the depths of your despair
Of course, the pronunciation of a sentence will never be the same twice. Here is the version I'm working from. It's from Youtube. This lyric begins at 1.26.
Two of the things that make Adele's singing interesting to listen to are that a) she uses a lot of genuine features of very modern regional London English pronunciation in her songs and doesn't usually convert to RP or an affected American accent, and b) she uses a lot of genuine features of connected speech, including weak forms, even though she is singing.
This means that you will hear many beautiful instances of glottal stops in between vowels, vocalised /l/s at the end of syllables and the occasional use of th-fronting amongst many other features.
So, if you're used to American English or other rhotic forms of English, one of the first things you will notice is that there are no /r/s pronounced at the end of the words your or despair. This is because South Eastern varieties of British English only pronounce /r/ when it occurs before a vowel.
You will also notice that the word of is pronounced with the same vowel that we find at the beginning and end of the word America, namely a schwa /ə/. This is the way this word always sounds when it isn't stressed or doesn't occur at the end of a sentence. It does not have the same vowel we hear in the word lot.
So far all of this is quite normal stuff. But there are three interesting aspects to the pronunciation of this sentence here. The first is an example of perseverative assimilation. I'll explain below:
The digraph "th" can represent the sound /θ/ which we find in the word think or theta. In grammatical words like this, that, then, these, those and so forth, however, it usually represents the sound /ð/ that we find in the word the. Now, very often in English when we get a word ending in /n/ followed by a word beginning with /ð/, both the /n/ and the /ð/ sounds change and become similar to each other. Consider:
Firstly the /n/ changes so that it moves from its normal position. We now make it on the back of our top teeth. Secondly, the /ð/ changes so that it becomes a nasal sound. In other words it also becomes an /n/ made on the back of our top teeth. So instead of saying:
We often say:
Remember though that both of those /n/ sounds will be made on the back of the top teeth. This is exactly what happens when Adele sings this lyric. She pronounces it like this:
The next thing you'll notice is that in the word depths we have a lovely example of th cluster simplification. This time it's the th we find in think not the one we find in those. The symbol we use to represent it is: /θ/. There is a phonological rule in English that when a word internal /θ/ sound is surrounded on either side by consonants, the /θ/ may be dropped (the technical word is elided). So for example, the word fifths, /fɪfθs/, is often pronounced "fifs", /fɪfs/. This is what we find in Adele's pronunciation of depths, which she pronounces perfectly correctly as /deps/.
The last thing is that Adele's vowel in the word your is a bit unusual. This might be an affectation from singing, or it might be part of her accent. Instead of pronouncing your with the vowel /ɔ:/ she seems to be using a glide, a diphthong, which we might represent as /ɔʊ/.
We might expect someone singing to pronounce this line like this:
- θɪŋk ɒv mi ɪn ði depθs ɒv jɔ: dɪspeə
However, Adele actually sings:
- θɪŋk əv mi ɪn nə deps əv jɔʊ dɪspeə
Best Answer
Sibilance is the word you're looking for.