Questions about the Taiwanese mandarin accent
There actually is a course that distinguishes Taiwan Mandarin from Mainland Chinese Mandarin: Glossika has both split into different courses, much as European and Brazilian Portuguese are distinguished as standard in most courses. 

One of the most salient basic phonological differences in standard Taiwan Mandarin 國語 vs standard PRC Mandarin 普通话 is ㄩㄥ vs yong. In Taiwan standard Mandarin it's yu- and -(e)ng, whilst in PRC standard Mandarin it's yi- plus -ong. However there's been some rapprochement happening between the two.

Another ㄥ related pronunciation issue relates to the quality of the vowel of after the labial consonants b-, p-, f-, m-: whereas PRC Mandarin uses a mid-back but relatively unrounded vowel [ɤ], whereas Taiwan Mandarin generally uses a slightly more closed but more rounded vowel [ʊ~u].

The Wikipedia article on Taiwanese Mandarin gives a quick run down. The merging of retroflex into alveolar is mentioned, as is the lack of erhua; additionally in Taiwanese Mandarin there is:


greater syllable-timed isochrony; syllables are regularly spaced, with much less difference between stressed and non-stressed syllables
as a corollary to the above, much less use of neutral tone


Then there are more basilectal forms of Taiwanese Mandarin, where the accent is strongly influenced by either Taiwanese Hokkien (Min Nan) or Taiwanese Hakka. This (the Hokkien version at least) is what is generally parodied as ㄉㄞˇ ㄨㄢ ㄍㄛˊ ㄧˇ (Dǎiwān góyǐ). You can see some of the phonological changes there: specific lexical interference from Hokkien on 臺, lack of certain glides, and the absence of the ㄩ phoneme (converting it consistently to ㄧ).