When I moved to Scotland and had to learn to understand the natives, I was of course aware of the existence of Scots, but I assumed (wrongly!) that people at any one time would normally speak either Scots or English (or rather, Scottish Standard English [SSE], which is standard English with a Scottish pronunciation and a few loanwords from Scots, such as wee, dreich, outwith and glaikit).
However, I was rather disappointed that I almost never met any speakers of Scots, and at the same time SSE speakers often seemed to mumble — for instance, foot sometimes sounded more like /fɪt/ than /fut/ [fyt] (the expected mapping of RP /fʊt/). Other examples included you sounding like /ji/ rather than /ju/, use (the verb) sounding like /jez/ rather than /juz/, dog sounding like /dʌg/ rather than /dɔg/, and thirty sounding like /θɛrte/ rather than /θɪrte/. Strangely, whenever I asked people to repeat one of these words, they invariably produced the vowel I had expected in the first instance (e.g., /fut/, never /fɪt/).
The alternative to my theory that all Scots were mumbling was to assume that the SSE phonemes had extremely varied and overlapping realisations — in other words, I speculated for a while that /u/ perhaps could be realised as [u, y, ɪ, i, e]! However, that’s obviously not true — while foot can be [fɪt], [fut] and [fyt], it can’t be *[fit] or *[fet], and so on.
Things didn’t click into place until I started learning Scots as a foreign language. When I learnt that the Scots words for foot, you and use were fit, ye and uise (pronounced as if it had been written yaize), it suddenly became clear that many SSE speakers were just using many more Scots words than I had realised, rather than mumbling English words as I had been assuming.
Once I had sussed this, several of my Scottish friends that I had till then perceived as mumbling SSE turned out to be speaking very clearly but using a lot of Scots words. In other words, not only had I been wrong about the mumbling, but I had also completely underestimated the usage of Scots — it’s just the case that it’s normally used mixed up with English rather than as a separate language.
Foreigners moving to Scotland should definitely learn some Scots. It’s not just the language of Burns and many other great poets, but it’s also currently mixed up with English in everyday conversations throughout Lowland Scotland, and it’s hard really to understand what people say without being bilingual in Scots and English like them.